Accurate Assessment of the State of Charge of Electrochemical Cells

ABSTRACT

Provided are methods, systems and devices for thermodynamically evaluating electrochemical systems and components thereof, including electrochemical cells such as batteries. The present systems and methods are capable of monitoring selected electrochemical cell conditions, such as temperature, open circuit voltage and/or composition, and carrying out measurements of a number of cell parameters, including open circuit voltage, time and temperature, with accuracies large enough to allow for precise determination of thermodynamic state functions and materials properties relating to the composition, phase, states of charge, health and safety and electrochemical properties of electrodes and electrolytes in an electrochemical cell. Thermodynamic measurement systems of the present invention are highly versatile and provide information for predicting a wide range of performance attributes for virtually any electrochemical system having an electrode pair.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of U.S. patent applicationSer. No. 13/871,454, filed on Apr. 26, 2013, which claims the benefit ofand priority to U.S. provisional application 61/639,712, filed on Apr.27, 2012, and this application also claims the benefit of and priorityto U.S. provisional application No. 62/081,959, filed on Nov. 19, 2014,each of which is hereby incorporated by reference in its entirety.

BACKGROUND

Over the last few decades, significant advances have been made inelectrochemical storage and conversion devices, expanding thecapabilities of these systems in a variety of fields including portableelectronic devices, air and space craft technologies, and biomedicaldevices. Current state of the art electrochemical storage and conversiondevices tend to have designs and performance attributes specificallyselected for compatibility with the diverse range of user applications.For example, current electrochemical storage systems span a range fromlight weight, stable batteries providing reliable, long runtimes to highcapacity batteries capable of providing extremely high discharge rates.Despite recent advances, widespread development and demand for highpower portable electronic products has created significant pressure forresearchers to develop even more high performance batteries suitable forthe wide range of these applications. Furthermore, demands ofminiaturization in the field of consumer electronics and instrumentationcontinue to stimulate research into novel design and material strategiesfor reducing the sizes, weights and form factors of high performancebatteries.

Many recent advances in electrochemical storage and conversiontechnology are directly attributable to discovery and integration of newmaterials for battery components. Lithium-ion battery technology, forexample, continues to rapidly develop, at least in part, due to theintegration of novel cathode and anode materials for these systems. Fromthe pioneering discovery and optimization of intercalated carbon anodematerials to more recent discoveries of nanostructured transition metaloxide intercalation cathode materials and nano-phosphate cathodematerials, development of new materials has revolutionized the designand performance capabilities of primary and secondary lithium ionbatteries. For example, advanced electrode materials have significantlyenhanced the energy capacities, energy densities, discharge currentrates and cycle life provided by these systems, thus positioning lithiumion batteries to be the preferred technology for the next generation ofhigh-power portable electronic systems, hybrid electric car (HEV) andelectric vehicles (EV). Advances in electrode materials also has greatpromise to positively impact other systems including electrochemicalcapacitors and supercapacitors, and fuel cells, and is likely to becritical to implementation of these technologies for a range of deviceapplications. Accordingly, the identification and performance evaluationof novel electrode materials is currently a research priority in thedevelopment of new and improved electrochemical energy storage andconversion systems.

Electrochemical energy storage and conversion devices use twoelectrodes; an anode and a cathode, which are electrical conductors,separated by a purely ionic conductor, the electrolyte. The electriccurrent generated during discharge results from chemical reactions andphysical processes (e.g., transport) taking place at the electrodes'surfaces, in which positively or negatively charged ions are exchangedwith the electrolyte. These processes, in turn, generate or absorbelectrons so as to keep the electrical neutrality of the system. Thecharge exchange induces important modifications in the electrodessurface and bulk structures properties. In particular, charge transferprocesses affect each electrode's potential and reaction rate, which setthe energy and the power density outputs of an electrochemical powergenerating device. In the case of a rechargeable battery, for example,the mechanism(s) and extent of changes in the electrodes surface andbulk structure determine the cycle life under specific thermodynamic andkinetic operating conditions (e.g., temperature, charge and dischargevoltage limits, current rates and so on).

Knowing the thermodynamics of electrode reactions and physicaltransformations is essential in predicting the performance and stabilityof any electrochemical storage and conversion system. For example,important thermodynamic state functions establish, at least in part, theenergy, the power and the cycle life of an autonomous electrochemicalpower source. In fact, the energy density reflects the total amounts ofcharges reversibly exchanged and the potential at which the exchangeoccurs. On the other hand, cycle life relates to the stability of statesor phases resulting from electrode transformations in the process ofcharge and discharge. All these processes are controlled, at least to acertain degree, by the thermodynamics of the electrode reactions.

A number of techniques have been developed and applied to evaluating thethermochemical kinetics of electrode reactions includingelectroanalytical methods (e.g., cyclic voltammetry, potentiometry etc.)and spectroscopic techniques (e.g. x-ray diffraction, NMR, LEEDs, etc.).Given the importance of thermodynamics in virtually all electrochemicalenergy storage and conversion systems, however, there is currently aneed in the art for systems and methods for measuring key thermodynamicparameters, such as changes in entropy, enthalpy and Gibbs free energy,with the accuracy needed for predicting and optimizing the performanceattributes and capabilities of these systems. Such systems would play asignificant role in identifying new materials for the next generation ofelectrochemical energy storage and conversion systems, and wouldsignificantly contribute to enhancing understanding of thethermochemical kinetics of established cathode and anode materials. Newthermodynamic analysis systems also have great potential as versatiletest instruments for characterizing materials properties and performancein commercially manufactured electrode systems, including batteries andfuel cells.

SUMMARY

The present invention provides systems and methods for accuratelycharacterizing thermodynamic and materials properties of electrodes andelectrochemical energy storage and conversion systems. Systems andmethods of the present invention are capable of simultaneouslycollecting a suite of measurements characterizing a plurality ofinterconnected electrochemical and thermodynamic parameters relating tothe electrode reaction state of advancement, voltage and temperature.Enhanced sensitivity provided by the present methods and systemscombined with measurement conditions that reflect or approximatethermodynamically stabilized electrode conditions allow very accuratemeasurement of thermodynamic parameters, including state functions suchas the Gibbs free energy, enthalpy and entropy ofelectrode/electrochemical cell reactions, that enable prediction ofimportant performance attributes of electrode materials andelectrochemical systems, such as the energy, power density, currentrate, state of health, state of safety and the cycle life of anelectrochemical cell.

The present systems and methods allow for the sensitive characterizationof properties of electrochemical cells related to performance and usage.The systems and methods herein utilize relationships between physicalproperties and thermodynamic parameters to determine properties relatedto electrochemical cell performance and usage such as state of charge,state of health and/or state of safety. The present systems and methods,for example, may utilize multidimensional profile analysis of physicalproperties and thermodynamic parameters to characterize the state ofcharge, state of health, and/or state of safety of an electrochemicalcell.

The systems and methods provided herein are versatile and may be used tocharacterize an electrochemical cell after manufacture or in situ whilethe electrochemical cell is in use. Advantageously, properties may bemeasured and results determined during normal operation of the device inwhich the electrochemical cell is powering. Parameters may be measuredwhile the device is powering up, powering down, in sleep mode, brakingor accelerating, or merely changes in temperature due to human contact.Multidimensional profiles used in conjunction with the present inventionmay be generated during manufacture and uploaded into systems or may begenerated by the systems and methods during normal electrochemical celloperation and periodically updated to account for changes inelectrochemical cell health.

In an aspect, the present invention provides a method for characterizingthe state of charge of an electrochemical cell comprising: (i)generating a multidimensional state of charge profile corresponding tothe electrochemical cell; (ii) measuring a plurality of open circuitvoltages of the electrochemical cell corresponding to a plurality oftemperatures of the electrochemical cell; (iii) determining a pluralityof thermodynamic parameters corresponding to the electrochemical cell,wherein the thermodynamic parameters are selected from the groupcomprising: a change in enthalpy (ΔH), a change in entropy (ΔS) and achange in free energy (ΔG); and (iv) characterizing the state of chargeof the electrochemical cell using the multidimensional state of chargeprofile and the thermodynamic parameters.

In embodiments, for example, the multidimensional state of chargeprofile is characterized prior to use of the electrochemical cell. Inembodiments, the multidimensional state of charge profile ischaracterized in situ during use of the electrochemical cell. In anembodiment, the method further comprises measuring the plurality oftemperatures of the electrochemical cell. In embodiments, themultidimensional state of charge profile is defined by at least threevariables, for example, a profile defined by at least state of charge,change in enthalpy (ΔH) and change in entropy (ΔS). In an embodiment,the multidimensional state of charge profile is a nonlinear functionrelating state of charge to change in enthalpy (ΔH) and change inentropy (ΔS), for example, wherein characterizing the state of charge ofthe electrochemical cell comprises comparing a change in enthalpy (ΔH)and a change in entropy (ΔS) determined for the electrochemical cell tothe multidimensional state of charge profile to determine the state ofchange of the electrochemical cell. In an embodiment, characterizing thestate of charge of the electrochemical cell comprises identifying thestate of charge corresponding to a change in enthalpy (ΔH) and a changein entropy (ΔS) determined for the electrochemical cell for themultidimensional state of charge profile.

In embodiments, for example, the step of generating a multidimensionalstate of charge profile comprises: (i) generating a plurality ofdifferent states of charge for the electrochemical cell; and (ii)measuring the thermodynamic parameters corresponding to each of theplurality of states of charge; wherein the thermodynamic parameters areselected from the group comprising: a change in enthalpy (ΔH), a changein entropy (ΔS) and a change in free energy (ΔG), thereby generating themultidimensional state of charge profile. In an embodiment, the step ofgenerating a plurality of states of charge is carried out stepwise byincreasing or decreasing the state of charge of the electrochemicalcell. In an embodiment, the step of generating a plurality of states ofcharge is carried out by discharging or charging the electrochemicalcell.

In embodiments, the states of charge are measured using a chargecalculating circuit. In an embodiment, for example, the plurality ofstates of charge are different coulometric states of charge of theelectrochemical cell. In an embodiment, the method of determining thestate of charge further comprises selectively adjusting the temperaturethe electrochemical cell so as to establish the plurality oftemperatures of the electrochemical cell. In an embodiment, theplurality of temperatures of the electrochemical cell are established byin situ temperatures changes of the electrochemical cell during use. Inan embodiment, the open circuit voltages of the electrochemical cell areeach independently measured to a margin of error less than or equal to0.1 mV, optionally less than or equal to 0.01 mV. In an embodiment, thetemperatures of the electrochemical cell are each independently measuredto a margin of error less than or equal to 0.1 K, optionally less thanor equal to 0.01 K.

In an embodiment, the open circuit voltages of the electrochemical cellindependently correspond to thermochemically stabilized conditions, forexample, wherein said temperatures are established to within 0.1 K, oroptionally to 0.01 K. In an embodiment, for example, the step ofmeasuring a plurality of open circuit voltages comprises independentlydetermining a plurality of observed rates of change in open circuitvoltage per unit time for each corresponding temperature. In anembodiment, an absolute value of the change in open circuit voltage perunit time is compared to a threshold open circuit voltage per unit timecorresponding to the temperature, wherein the thermochemicallystabilized conditions correspond to conditions of the absolute value ofthe change in open circuit voltage per unit time less than the thresholdopen circuit voltage per unit time, for example, a threshold opencircuit voltage per unit time less than or equal to 1.0 mV h⁻¹, 0.1 mVh⁻¹, or, optionally, 0.01 mV h⁻¹.

In an embodiment, the invention further provides a method fordetermining a state of health or a state of safety of theelectrochemical cell using the state of charge determined for theelectrochemical cell. In an embodiment, the state of health isdetermined by comparing the determined state of charge with a thresholdstate of charge, wherein the threshold state of charge is a maximumstate of charge from an electrochemical cell provided in a newcondition. In an embodiment, the state of safety is determined by usingthe state of charge and the temperature to calculate the probability ofa thermal runaway corresponding to the electrochemical cell, wherein thestate of safety is a function of the probability of a thermal runaway.In an embodiment, for example the temperature analyzer further comprisesa temperature controller for adjusting the temperature of theelectrochemical cell.

In an aspect, the present invention provides a measurement system forthermodynamically characterizing a state of charge of an electrochemicalcell comprising: (i) a temperature analyzer for measuring or receivingtemperature measurements of said electrochemical cell; (ii) an opencircuit voltage analyzer for measuring open circuit voltagescorresponding to a plurality of different temperatures of saidelectrochemical cell, for example, a plurality of temperatures differentby at least 0.1 K or at least 0.5 K or a plurality of temperatureshaving a difference range of between 0.01 K and 5 K; (iii) athermodynamic parameter processor positioned in data communication withsaid temperature analyzer and said open circuit voltage analyzer, theprocessor programmed to determine thermodynamic parameters based on theopen circuit voltage measurements and the temperature measurements;wherein the thermodynamic parameters are selected from the groupcomprising: a change in enthalpy (ΔH), a change in entropy (ΔS) and achange in free energy (ΔG); and (iv) a state of charge processorpositioned in data communication with said temperature analyzer and saidopen circuit voltage analyzer, the processor programmed to characterizethe state of charge of the electrochemical cell using the plurality ofthe thermodynamic parameters and a multidimensional state of chargeprofile. In an embodiment, the systems further comprises a currentanalyzer for measuring charging and discharging current forcharacterizing the multidimensional state of charge profilecorresponding to the electrochemical cell.

In an embodiment, the multidimensional state of charge profile ischaracterized prior to use of the electrochemical cell. Optionally, inan embodiment, the multidimensional state of charge profile ischaracterized in situ during use of the electrochemical cell. In anembodiment, the multidimensional state of charge profile is a defined byat least three variables, for example, at least state of charge, changein enthalpy (ΔH) and change in entropy (ΔS). In an embodiment, forexample, the multidimensional state of charge profile is a nonlinearfunction relating state of charge to change in enthalpy (ΔH) and changein entropy (ΔS). In an embodiment, the processor characterizes the stateof charge of the electrochemical cell by comparing a change in enthalpy(ΔH) and a change in entropy (ΔS) determined for the electrochemicalcell to the multidimensional state of charge profile to determine thestate of charge of the electrical cell. In embodiments, for example, theprocessor characterizes the state of charge of the electrochemical cellby identifying the state of charge corresponding to a change in enthalpy(ΔH) and a change in entropy (ΔS) determined for the electrochemicalcell for the multidimensional state of charge profile.

In an embodiment, the system of the present invention is embedded intothe electrochemical cell. In an embodiment, the system is connected tothe electrochemical cell or contained within a housing of theelectrochemical cell. In embodiments, the system is positioned inselective data or selective electrical communication with one or moreelectrochemical cells; or wherein the device is positioned in switchabledata communication or switchable electrical communication with one ormore electrochemical cells, or for example, in wireless datacommunication or wireless electrical communication with theelectrochemical cell.

In an embodiment, the processor programmed to determine thermodynamicparameters and the processor programmed to characterize state of chargeare a single processor. In an embodiment, the system is an integratedcircuit. In embodiments, the system further comprises a temperaturesensor. In embodiments, the system further comprises a currentcontroller, wherein the current controller generates a plurality ofdifferent states of charge for the electrochemical cell and theprocessor measures the thermodynamic parameters corresponding to each ofthe plurality of the states of charge and generates a multidimensionalstate of charge profile. In an embodiment, for example, the currentcontroller generates a plurality of states of charge by stepwiseincreasing or decreasing the state of charge of the electrochemicalcell.

In embodiments, the temperature analyzer measures said temperature ofsaid electrochemical cell within a margin of error of less than or equalto 0.1 K, optionally a margin of error of less than or equal to 0.01 K.In embodiments, the open circuit voltage analyzer measures saidtemperature of said electrochemical cell within a margin of error ofless than or equal to 0.1 mV, optionally a margin of error less than orequal to 0.01 mV. In embodiments, for example, the open circuit voltageanalyzer measures open circuit voltages corresponding tothermochemically stabilized conditions. In an embodiment, the opencircuit voltage analyzer independently measures rates of change in opencircuit voltage per unit time for each corresponding temperature. In anembodiment, an absolute value of said change in open circuit voltage perunit time is compared to a threshold open circuit voltage per unit timecorresponding to said temperature, wherein said thermochemicallystabilized conditions correspond to conditions of said absolute value ofsaid change in open circuit voltage per unit time less than saidthreshold open circuit voltage per unit time, for example, a thresholdopen circuit voltage per unit time less than or equal to 1.0 mV h⁻¹, 0.1mV h⁻¹, or, optionally, 0.01 mV h⁻¹.

In an embodiment, systems of the present invention further determine astate of health or a state of safety of the electrochemical cell usingthe state of charge determined by the system. In an embodiment, thesystem determines state of health by comparing the determined state ofcharge with a threshold state of charge, wherein the threshold state ofcharge is a maximum state of charge from an electrochemical cellprovided in a new condition. In an embodiment, system determines stateof safety by using the state of charge and the temperature to calculatethe probability of a thermal runaway corresponding to theelectrochemical cell, wherein the state of safety is a function of theprobability of a thermal runaway.

In an aspect, the present invention provides a device for monitoring thestate of charge of an electrochemical cell, said device comprising: (i)a temperature monitoring circuit for measuring a plurality oftemperatures of said electrochemical cell; (ii) a voltage monitoringcircuit for measuring a plurality of open circuit voltages of saidelectrochemical cell corresponding to said plurality of temperatures,said plurality of open circuit voltages generated upon charging ordischarging said electrochemical cell or stopping charging ordischarging said electrochemical cell; (iii) a thermodynamic measurementcircuit for determining thermodynamic parameters of said electrochemicalcell, wherein said thermodynamic parameters are change in enthalpy (ΔH)of said electrochemical cell, a change in entropy (ΔS) of saidelectrochemical cell and/or a change in free energy of saidelectrochemical cell (ΔG); wherein said thermodynamic measurementcircuit is positioned in electrical or data communication with saidvoltage monitoring circuit to receive said open circuit voltagemeasurements and positioned in electrical or data communication withsaid temperature monitoring circuit to receive said temperatures; and(iv) a state of charge calculating circuit for determining the state ofcharge of said electrochemical cell positioned in electrical or datacommunication with said thermodynamic circuit to receive saidthermodynamic parameters; wherein said state of charge calculatingcircuit determines a state of charge of said electrochemical cell usingsaid thermodynamic parameters and a multidimensional state of chargeprofile for said electrochemical cell.

In embodiments, for example, at least a portion of the temperaturemonitoring circuit, voltage monitoring circuit, thermodynamicmeasurement circuit, and state of charge calculating circuit compriseone or more integrated circuits. In an embodiment, all of thetemperature monitoring circuit, voltage monitoring circuit,thermodynamic measurement circuit, and state of charge calculatingcircuit comprise a single integrated circuit. In an embodiment, thedevice further comprises a current monitoring circuit for measuring acharging current of the electrochemical cell or a discharging circuitcurrent of the electrochemical cell, wherein the current monitoringcircuit is positioned in electronic or data communication with thethermodynamic circuit and the state of charge generating circuit.

In an embodiment, for example, the device determines a true state ofcharge of an electrochemical cell. In embodiments, the thermodynamicmeasurement circuit determines a change in enthalpy (ΔH) and a change inentropy (ΔS) for the electrochemical cell. In embodiments, the state ofcharge calculating circuit compares the change in enthalpy (ΔH) and thechange in entropy (ΔS) determined for the electrochemical cell to themultidimensional state of charge profile. In an embodiment, for examplethe state of charge calculating circuit identifies the state of chargecorresponding to the change in enthalpy (ΔH) and the change in entropy(ΔS) determined for the electrochemical cell to the multidimensionalstate of charge profile.

In an embodiment, the device is embedded into said electrochemical cell.In an embodiment, the device is attached to said electrochemical cell orcontained within a housing of said electrochemical cell. Optionally, inan embodiment, the device is in wireless data communication or wirelesselectrical communication with said electrochemical cell.

The present systems and methods also allow sensitive characterization ofthe composition, phase and materials properties important for design andperformance of electrodes in electrochemical systems. The presentmethods enable identification and characterization of phase transitions,crystallite size, surface and bulk defects and crystal structure defectsin electrode materials that dramatically impact the electrochemicalproperties of electrodes and the performance of electrochemical storageand conversion systems. For example, thermodynamic state functions canbe measured by the present systems and methods with an accuracy thatenables identification of major or small phase transformations, whichmay be difficult, if not impossible, to detect via conventional meanssuch as x-ray diffractometry or simple open-circuit cell potentialmeasurements. Some small transformations may be the onset or the preludeof more drastic ones, which upon prolonged cycling will affect thebattery's energy, power and cycle life performances. Detection of suchtransformations and understanding their origin is crucial for optimizedelectrode materials design.

Systems and methods of the present invention are also applicable forcharacterizing a range of thermodynamic parameters useful for designing,testing and characterizing electrochemical cells, such as primary andsecondary batteries and electrode materials, including but not limitedto intercalating electrode materials. The capabilities of the presentsystems and methods, however, extend beyond batteries and encompasselectrode reactions in other electrochemical devices/systems includingfuel cells, EDLCs, gas electrodes, catalysis, corrosions,electro-deposition, and electrosynthesis, where the acquisition ofthermodynamics data also provides important insights on the energeticsof electrode reactions and device performance.

In one aspect, provided are devices for monitoring a condition of anelectrochemical cell. A device of this aspect comprises an integratedcircuit comprising a voltage monitoring circuit for measuring aplurality of open circuit voltages of an electrochemical cell, atemperature monitoring circuit for measuring a plurality of temperaturesof the electrochemical cell, a current monitoring circuit for measuringa charging current or a discharging current of the electrochemical celland a circuit for determining a thermodynamic parameter of theelectrochemical cell. In embodiments, one or more of a plurality of opencircuit voltages and a plurality of temperatures of the electrochemicalcell are generated upon charging or discharging the electrochemical cellor upon stopping a charging or discharging of the electrochemical cell.Useful thermodynamic parameters include one or more of a change inentropy (ΔS) of the electrochemical cell, a differential entropy (dS) ofthe electrochemical cell, a change in enthalpy (ΔH) of theelectrochemical cell, a differential enthalpy (dH) of theelectrochemical cell and a change in free energy (ΔG) of theelectrochemical cell.

In embodiments, the circuit for determining a thermodynamic parameter ispositioned in electrical or data communication with the temperaturemonitoring circuit to receive temperature measurements from thetemperature monitoring circuit. In embodiments, the circuit fordetermining a thermodynamic parameter is positioned in electrical ordata communication with the voltage monitoring circuit to receive opencircuit voltage measurements from the voltage monitoring circuit. Inembodiments, the circuit for determining a thermodynamic parameter ispositioned in electrical or data communication with the currentmonitoring circuit to receive current measurements from the currentmonitoring circuit or to provide thermodynamics parameters to thecurrent monitoring circuit.

Optionally, a device of this aspect is a component of an electrochemicalcell or is imbedded in the electrochemical cell. Imbedded devices andbattery systems of this nature are beneficial, for example, as they canbe used as a self-analyzing battery, battery system or battery packageor as a component of a larger system. Imbedded devices and batterysystems also provide the benefit of the ability to quickly andefficiently diagnose and characterize individual cells within amulti-cell battery system, such as to diagnose and identify cells thatare malfunctioning, improperly charging or discharging, unsafe, suitablefor removal or replacement, or to characterize one or more cell's cyclenumber, state of health or state of safety. Optionally, electrochemicalcells useful with the devices and methods described herein comprise twoor more electrodes, such as a cathode, an anode and, optionally, one ormore reference electrodes. Use of electrochemical cells comprising oneor more reference electrodes, in embodiments, provides for directlydetermining a condition of each electrode individually.

In embodiments, devices of this aspect are positioned so that the deviceand any associated components are not corroded or degraded, for exampleby exposure to components of an electrochemical cell. Preventingcorrosion and degradation is useful, for example, to provide fordurability of the device and any associated components, such as printedcircuit boards, resistors, capacitors, inductors and other circuitcomponents. In embodiments, the device is mounted on a printed circuitboard or, optionally, the device is mounted on a flexible circuit board.In certain embodiments, the device is mounted on a flexible circuitboard that is wrapped at least partially around an electrochemical cell.Optionally, the device comprises one or more resistors, capacitors andinductors positioned in electrical communication with one or morecomponents of the integrated circuit. In an exemplary embodiment, adevice of this aspect is positioned in electrical communication with oneor more of an anode and a cathode of an electrochemical cell, forexample by one or more wires positioned to provide electricalcommunication between the device and the anode or cathode.

Optionally, devices of this aspect comprise a wireless transceivercircuit, for example positioned in data communication or electricalcommunication with one or more components of the device or of theintegrated circuit. In a specific embodiment, a device of this aspectcomprises one or more wireless transceivers providing data communicationbetween components of the device, such as between one or more of thevoltage monitoring circuit, the temperature monitoring circuit, thecurrent monitoring circuit the circuit for determining a thermodynamicparameter and other circuits of the devices of this aspect. Includingwireless transceivers in devices of this aspect provides, for example,for flexibility in the design and configuration of the devices.

In a specific embodiment, the device and optional circuit components,such as inductors, capacitors, resistors and external circuitcomponents, are surface mount type components. In embodiments, thedevice and optional circuit components have a thickness of 5 mm or less,3 mm or less or 2 mm or less. Optionally, the device is attached to anelectrochemical cell between fabrication of the electrochemical cell andpackaging of the electrochemical cell.

In one embodiment, for example, the device itself further comprises theelectrochemical cell. In one embodiment, for example, the device is acomponent of a package comprising the device and one or moreelectrochemical cells, such as in a battery pack. In certainembodiments, the device is positioned in selective data communication,selective electrical communication, switchable data communication orswitchable electrical communication with one or more electrochemicalcells. In another embodiment, the device is positioned outside a housingof the electrochemical cell or outside a package comprising theelectrochemical cell.

In embodiments, the integrated circuit of devices of this aspectcomprises a circuit for determining an open circuit state of anelectrochemical cell, for example a current monitoring circuit.Optionally, the integrated circuit comprises a power switching circuitand the power switching circuit optionally determines an open circuitstate of the electrochemical cell. In a specific embodiment, the circuitfor determining an open circuit state is configured to provide anindication, such as a data or voltage indication, to the voltagemonitoring circuit to measure the open circuit voltage of theelectrochemical cell when the electrochemical cell is in an open circuitvoltage state or operating under open circuit voltage conditions.Optionally, the circuit for determining an open circuit state isconfigured to provide an indication to one or more of a voltagemonitoring circuit, a temperature monitoring circuit and a currentmonitoring circuit to stop measuring an open circuit voltage, atemperature or a current of the electrochemical cell after a preselectedtime period. Optionally, the circuit for determining an open circuitstate is configured to provide an indication to one or more of a voltagemonitoring circuit, a temperature monitoring circuit and a currentmonitoring circuit to measure or re-measure an open circuit voltage, atemperature or a current of the electrochemical cell after a preselectedtime period. Thus, devices of this aspect optionally can detect when thecell is open circuit and then can measure the open circuit voltageimmediately, thereby improving measurement accuracy and determining whenthe electrochemical cell or a device comprising the electrochemical cellis powered off or shut down and thereby disable devices of this aspectfrom draining energy from the electrochemical cell.

Optionally, devices of this aspect do not directly or actively controlthe temperature of the electrochemical cell. Devices which do notdirectly control the temperature of the electrochemical cell are useful,for example, to minimize the number of components and complexity ofoperation of the system. Devices which do not directly control thetemperature of the electrochemical cell are beneficial as they do notrequire long times for establishing the temperature of anelectrochemical cell, but can still efficiently characterize and analyzeone or more conditions of the cell, such as a thermodynamic parameter,taking advantage of the changes in a temperature of the cell that occurduring charging and discharging or which occur after charging ordischarging is stopped as the cell temperature proceeds to the ambienttemperature due to passive heat exchange between the cell and the air orenvironment. Advantages gained from not including a temperaturecontroller and related components include, but are not limited to,minimizing the size of the device, minimizing the cost of the device,simplification of the complexity of the device. One benefit of thedevices of this aspect that do not directly or actively control thetemperature of the electrochemical cell is that they are capable ofdetermining one or more thermodynamic parameters of an electrochemicalcell, regardless of the ability to control the electrochemical celltemperature. An additional benefit of the devices of this aspect of thethat do not directly or actively control the temperature of theelectrochemical cell results from a reduced time for acquiring andprocessing an electrochemical cell's temperature, voltage, OCV,thermodynamic parameters, such as ΔS and ΔH, and state of charge andstate of health data. Such a reduction in acquisition and processingtime is advantageous, for example, because the data can be collectedmore frequently and does not require the time necessary for waiting forthe electrochemical cell's temperature to stabilize to the controlledtemperature.

For example, in one embodiment, the device does not comprise atemperature controller or a means for controlling or establishing atemperature of the electrochemical cell, such as a heating element or anelement that transfers heat into the electrochemical cell by conductionfrom an external heat source, or a cooling element, such as athermoelectric cooler, a Peltier cooler or an element that activelytransports heat out of the electrochemical cell by conduction to anexternal heat sink. In an embodiment, for example the device does notcomprise a temperature controller or a means for actively controlling orestablishing a temperature of the electrochemical cell. In anembodiment, for example the device does not comprise a temperaturecontroller or a means for actively controlling or establishing aspecified or selected temperature of the electrochemical cell.

In certain embodiments, however, an electrochemical cell comprises or isin thermal communication with one or more heat sinks, heat exchangers,liquid cooling or air cooling systems or heat pipes, even when a deviceof this aspect does not directly control the temperature of theelectrochemical cell. Heat sinks, heat exchangers, liquid cooling or aircooling systems or heat pipes are optionally used to maintain thetemperature of an electrochemical cell within a selected working rangeor to prevent the temperature of an electrochemical cell from risingbeyond a specified, maximum, or rated temperature. Use of a heat sink,heat exchanger, liquid cooling or air cooling system or heat pipepermits more efficient heat transfer between an electrochemical cell andthe environment than by passive transport of heat than if a heat sink,heat exchanger or heat pipe were not used. In certain embodiments, aheat sink or heat exchanger is positioned such that air is moved acrossthe heat sink or heat exchanger to facilitate passive heat transport tothe air or environment. Optionally, a liquid cooling or air coolingsystem or heat pipe is used to transport heat between an electrochemicalcell and a heat sink or heat exchanger. In certain embodiments, a liquidcooling or air cooling system or heat pipe is positioned such that heatis transported using the liquid cooling or air cooling system or heatpipe to a remotely located heat sink or heat exchanger to facilitatepassive heat transport to the air or environment.

Other useful temperature regulating systems include forced air coolingsystems (e.g., fan driven systems), compressed air cooling systems andheat exchangers using high heat exchange surface areas and fast heattransfer materials, such as copper or aluminum. A heat exchangeroptionally comprises a cooling fluid such as compressed air, cooledwater, a phase transition heat absorbent or a heat transferring materialsuch as a liquid metal or a molten salt.

Optionally, a device of this aspect further comprises a temperaturesensor positioned in thermal communication with the electrochemical celland also positioned in electrical or data communication with thetemperature monitoring circuit. Optionally, the temperature monitoringcircuit determines or monitors a temperature of the electrochemical cellas the electrochemical cell is charging or discharging. Optionally, thetemperature monitoring circuit determines or monitors a temperature ofthe electrochemical cell when the electrochemical cell is not chargingor when the electrochemical cell is not discharging. Useful temperaturesensors include those comprising thermocouples, resistance thermometersand thermistors.

Optionally, a device of this aspect is a component of an automobile,such as an electric vehicle or a hybrid electric vehicle. Incorporationof devices of this aspect into automobiles is beneficial to permitmonitoring and characterizing of the electrochemical cells used to drivean electric motor in an automobile. Optionally, in devices of thisaspect that comprise a component of an automobile, the voltagemonitoring circuit measures a plurality of open circuit voltages of theelectrochemical cell when the automobile is idle, stopped, parked,powered off, powering off, powered on, powering on, accelerating ordecelerating. Optionally, in devices of this aspect that comprise acomponent of an automobile, the temperature monitoring circuit measuresa plurality of temperatures of the electrochemical cell when theautomobile is idle, stopped, parked, powered off, powering off, poweredon, powering on, accelerating or decelerating.

In embodiments, a change in open circuit voltage of the electrochemicalcell occurs when the automobile is idle, stopped, parked, powered off,powering off, powered on, powering on, accelerating or decelerating. Inembodiments, a change in temperature of the electrochemical cell occurswhen the automobile is idle, stopped, parked, powered off, powering off,powered on or powering on off, powered on, powering on, accelerating ordecelerating. Optionally, a plurality of temperatures of theelectrochemical cell are measured during or after one or more of idlingof the automobile, stopping the automobile, parking the automobile,powering off the automobile, powering on the automobile, acceleratingthe automobile, and decelerating the automobile. Optionally, a pluralityof open circuit voltages of the electrochemical cell are measured duringor after one or more of idling of the automobile, stopping theautomobile, parking the automobile, powering off the automobile,powering on the automobile, accelerating the automobile, anddecelerating the automobile.

Optionally, a device of this aspect is a component of a mobile orportable electronic device, such as a cell phone, a laptop computer, atablet computer, an e-book reader, a portable music player, a portableaudio player, a portable video player, a bar code reader, a telemetricreader, a portable light device, a portable sound or alarm device, aportable autonomous electric power devices, such as for military,telecommunications, aerospace and space applications, games, watches,clocks, portable medical devices, implantable medical devices.Optionally, a device of this aspect is a component of a stationary,though portable, electronic device, such as a gas detector, a smokedetector or an alarm system. Incorporation of devices of this aspectinto mobile and portable electronic devices is beneficial to permitmonitoring and characterizing of the electrochemical cells used to powerthe mobile or portable electronic device. Optionally, in devices of thisaspect that comprise a component of a mobile or portable electronicdevice, the voltage monitoring circuit measures a plurality of opencircuit voltages of the electrochemical cell when the portableelectronic device is idle, powered off, powering off, powered on orpowering on. Optionally, in devices of this aspect that comprise acomponent of a mobile or portable electronic device, the temperaturemonitoring circuit measures a plurality of temperatures of theelectrochemical cell when the portable electronic device is idle,powered off, powering off, powered on or powering on.

In embodiments, a change in open circuit voltage of the electrochemicalcell occurs when the portable electronic device is idle, powered off,powering off, powered on or powering on. In embodiments, a change intemperature of the electrochemical cell occurs when the portableelectronic device is idle, powered off, powering off, powered on orpowering on. Optionally, a plurality of temperatures of theelectrochemical cell are measured during or after one or more of idlingof the portable electronic device, powering off the portable electronicdevice and powering on the portable electronic device. Optionally, aplurality of open circuit voltages of the electrochemical cell aremeasured during or after one or more of idling of the portableelectronic device, powering off the portable electronic device andpowering on the portable electronic device.

Optionally, a device of this aspect is a component of a battery backupsystem, such as an uninterruptable power supply. Optionally, a device ofthis aspect is a component of a stationary energy storage system orfacility, such as those attached to photovoltaic, wind, geothermal,hydraulic and tide energy generating systems and generally for electricpower plants. Incorporation of devices of this aspect into these andother systems is beneficial to permit monitoring and characterizing ofthe electrochemical cells used in battery backup systems, load levelingsystems and peak shaving systems.

In embodiments, devices of this aspect are useful determining athermodynamic parameter of the electrochemical cell. In a specificembodiment, the thermodynamic parameter of the electrochemical cell isdetermined using one or more of the plurality of open circuit voltagesof the electrochemical cell the plurality of temperatures of theelectrochemical cell. For example, in an embodiment, a change in freeenergy of the electrochemical cell is determined by measuring an opencircuit voltage of the electrochemical cell. In an embodiment, forexample, a change in enthalpy of the electrochemical cell is determinedby measuring an open circuit voltage of the electrochemical cell at aplurality of temperatures. Optionally, a change in enthalpy of theelectrochemical cell is determined by computing an intercept of a linearregression of open circuit voltage measurements of the electrochemicalcell versus temperature measurements of the electrochemical cell. In anembodiment, for example, a change in entropy of the electrochemical cellis determined by measuring an open circuit voltage of theelectrochemical cell at a plurality of temperatures. Optionally, achange in entropy of the electrochemical cell is determined by computinga slope of a linear regression of open circuit voltage measurements ofthe electrochemical cell versus temperature measurements of theelectrochemical cell.

In embodiments, different temperatures of the electrochemical cell areachieved through the temperature changes that naturally occur throughuse of the electrochemical cell, for example by charging or discharging.In embodiments, the temperature of an electrochemical cell increases asthe electrochemical cell is charged or discharged. Conversely, inembodiments, the temperature of an electrochemical cell decreases aftercharging or discharging of the electrochemical cell stops. Such naturaltemperature changes are used by the devices and methods of the presentinvention for determining one or more thermodynamic parameters.

Although it may not uniformly be the case for all electrochemical cellchemistries, in embodiments, the open circuit voltage for anelectrochemical cell increases as the temperature of the electrochemicalcell increases or decreases as the temperature of the electrochemicalcell decreases. In many embodiments, the open circuit voltage of anelectrochemical cell changes as the electrochemical cell is charged ordischarged. In some embodiments, the open circuit voltage of anelectrochemical cell changes after charging or discharging of theelectrochemical cell stops.

In embodiments, a thermodynamic parameter of the electrochemical cell isdetermined using a first temperature of the electrochemical cell and asecond temperature of the electrochemical cell different from the firsttemperature of the electrochemical cell. Optionally, a thermodynamicparameter of the electrochemical cell is determined using a firsttemperature of the electrochemical cell and a second temperature of theelectrochemical cell after the electrochemical cell is heated bycharging or discharging. Optionally, a thermodynamic parameter of theelectrochemical cell is determined using a first temperature of theelectrochemical cell and a second temperature of the electrochemicalcell after the electrochemical cell cools from the first temperature.

In embodiments, a thermodynamic parameter of the electrochemical cell isdetermined using a first open circuit voltage of the electrochemicalcell and a second open circuit voltage of the electrochemical celldifferent from the first open circuit voltage of the electrochemicalcell. For example, a thermodynamic parameter of the electrochemical cellis optionally determined using a first open circuit voltage of theelectrochemical cell and a second open circuit voltage of theelectrochemical cell after the electrochemical cell is charged ordischarged. For example, a thermodynamic parameter of theelectrochemical cell is optionally determined using a first open circuitvoltage of the electrochemical cell after charging or discharging of theelectrochemical cell is stopped and a second open circuit voltage of theelectrochemical cell while charging or discharging of theelectrochemical cell remains stopped and after the temperature of theelectrochemical cell changes.

Optionally, for a device of this aspect, the integrated circuit furthercomprises a state of charge calculating circuit for determining a stateof charge of the electrochemical cell. In embodiments, a state of chargecalculating circuit comprises a current measuring circuit. Monitoring,calculating and determination of the state of charge of anelectrochemical cell can be useful, in embodiments, for determination ofone or more conditions of the electrochemical cell. For example, a stateof health, charge cycle, or a state of safety can optionally bedetermined through a plurality of measurements or determinations ofelectrochemical cell state of charge. In some embodiments, the state ofhealth, charge cycle or state of safety of the electrochemical cell isdetermined by comparing a state of charge of the electrochemical cellwith one or more thermodynamic parameters of the electrochemical cell orby computing a linear or other regression of the state of charge of theelectrochemical cell versus one or more thermodynamic parameters of theelectrochemical cell. In embodiments, a plurality of states of charge ofthe electrochemical cell are generated upon charging or discharging theelectrochemical cell. In embodiments, the circuit for determining athermodynamic parameter is positioned in electrical or datacommunication with the state of charge calculating circuit to receivestate of charge measurements from the state of charge calculatingcircuit or to provide thermodynamic parameters to the state of chargecalculating circuit.

In embodiments, the state of charge of the electrochemical cell refersto a ratio of a first value to a second value. In one specificembodiment, the first value is a net amount of charge remaining in theelectrochemical cell and the second value is a rated charge capacity ofthe electrochemical cell or a theoretical charge capacity of theelectrochemical cell. In another specific embodiment, the first value isa net amount of charge required to charge the electrochemical cell to arated charge capacity of the electrochemical cell or to a theoreticalcharge capacity of the electrochemical cell and the second value is therated charge capacity of the electrochemical cell or the theoreticalcharge capacity of the electrochemical cell.

In one embodiment, a state of charge calculating circuit determines acoulometric state of charge of an electrochemical cell, for example,based on current measurements received from a current measuring circuit.In an embodiment, a state of charge calculating circuit determines atrue state of charge of an electrochemical cell based on thermodynamicparameters received by the state of charge calculating circuit.Optionally, the true state of charge of the electrochemical cell isdetermined by looking up received thermodynamic parameters in a look uptable or interpolating between points in a look up table. In a specificembodiment, the integrated circuit of devices of this aspect monitors anelectrochemical cell as it is charged under controlled conditions andthe integrated circuit updates entries in a look up table as theelectrochemical cell is charged. For example, during charging of anelectrochemical cell under controlled conditions, entries in the lookuptable, such as states of charge, open circuit voltages and thermodynamicparameters are updated.

Devices of this aspect include voltage monitoring circuits formeasuring, determining and/or estimating an open circuit voltage of anelectrochemical cell. Measurements or estimates of an open circuitvoltage of an electrochemical cell are useful for a variety of purposes,including determining a condition of an electrochemical cell, such as athermodynamic parameter of the electrochemical cell, a state of chargeof the electrochemical cell, a state of health of the electrochemicalcell, a state of safety of the electrochemical cell and a cycle numberof the electrochemical cell. In embodiments, open circuit voltagemeasurements or estimates provide insight into the electrochemicalcell's usage, safety, health, duration, durability and remaining life.In embodiments, open circuit voltage measurements or estimates provideinsight into the physical construction and or distribution of materialsand components within an electrochemical cell, such as to indicate aphase or components of the electrochemical cell, a composition ofcomponents of the electrochemical cell, or an event or condition takingplace within the electrochemical cell.

In embodiments, a device of this aspect measures or monitors an opencircuit voltage of an electrochemical cell, for example, using thevoltage monitoring circuit. Optionally, the voltage monitoring circuitdetermines an open circuit voltage of the electrochemical cell when theelectrochemical cell is not charging or when the electrochemical cell isnot discharging. Optionally, the voltage monitoring circuit determinesan open circuit voltage of the electrochemical cell after a charging ordischarging of the electrochemical cell is stopped. Optionally, thevoltage monitoring circuit determines an open circuit voltage of theelectrochemical cell for thermochemically stabilized conditions of theelectrochemical cell. Optionally, the voltage monitoring circuitdetermines an open circuit voltage of the electrochemical cell fornon-thermochemically stabilized conditions of the electrochemical cell.

In certain embodiments, it may require significant time for anelectrochemical cell to relax to thermochemically stabilized conditions,for example a time period longer than one second, longer than tenseconds, longer than thirty seconds, etc. Devices of this aspect arecapable of estimating an open circuit voltage of an electrochemical cellfor thermochemically stabilized conditions by monitoring changes in theopen circuit voltage of the electrochemical cell as the electrochemicalcell relaxes towards thermochemically stabilized conditions over ashorter time period than required for the electrochemical cell to fullyrelax to a thermochemically stabilized condition. For example, in someembodiments, the relaxation of open circuit voltage follows anexponential decay towards the open circuit voltage corresponding tothermochemically stabilized conditions. Monitoring the open circuitvoltage and computing the exponential decay time constant therebypermits calculation of the asymptotic open circuit voltage correspondingto thermochemically stabilized conditions. In an embodiment, the voltagemonitoring circuit determines or estimates an open circuit voltage ofthe electrochemical cell for thermochemically stabilized conditions ofthe electrochemical cell based on the open circuit voltage of theelectrochemical cell for the non-thermochemically stabilized conditionsof the electrochemical cell. This latter embodiment is useful, forexample, for situations where it takes time for the electrochemical cellto relax to thermochemically stabilized conditions.

Optionally, devices of this aspect are useful for monitoring one or moreconditions of an electrochemical cell, for example, a thermodynamicparameter, a state of health, a state of safety and a cycle number ofthe electrochemical cell. Monitoring one or more of these conditionspermits, for example, detailed information about the electrochemicalcell's usage, safety, health, duration, durability and remaining life.Such monitoring, for example, facilitates replacement of failing oraging electrochemical cells, as well as warning of imminent failure ordegraded performance of an electrochemical cell, thereby preventingcatastrophic failure of an electrochemical cell or a system drawingpower from the electrochemical cell.

In a specific embodiment, the integrated circuit of a device of thisaspect is configured to monitor a condition of one or moreelectrochemical cells, wherein the condition is one or more of athermodynamic parameter, a state of health, a state of safety and acycle number. In an embodiment, the circuit for determining athermodynamic parameter of the electrochemical cell further determinesone or more of a state of health of the electrochemical cell, a state ofsafety of the electrochemical cell and a cycle number of theelectrochemical cell.

Optionally, the integrated circuit further comprises an additionalcircuit for determining one or more of a state of health of theelectrochemical cell, a state of safety of the electrochemical cell anda cycle number of the electrochemical cell. Optionally, a device of thisaspect further comprises an additional circuit for determining one ormore of a state of health of the electrochemical cell, a state of safetyof the electrochemical cell and a cycle number of the electrochemicalcell, for example as a component external to the integrated circuit.

Useful conditions for monitoring of electrochemical cells include, butare not limited to, a thermodynamic parameter of the electrochemicalcell, a state of charge of the electrochemical cell, a state of healthof the electrochemical cell, a state of safety of the electrochemicalcell and a cycle number of the electrochemical cell. In embodiments, thestate of health of the electrochemical cell refers to the amount ofenergy (W·h) and power (W) deliverable or available in a system comparedto the best, ideal, theoretical or rated amounts when the system isnewly fabricated and tested, such as at 100% state of charge. Inembodiments, battery state of health decays or reductions result fromelectrode and electrolyte materials degradation, from an increase ininternal resistance and from mechanical and chemical effects, such ashardware deformation due to heat, gazing and corrosion. In embodiments,a metric for state of health assessment is the relative peak power fadeat a specified or defined state of charge, such as expressed bySOH=100(P(SOC)/P₀(SOC)), where, SOH refers to the state of health of theelectrochemical cell, P(SOC) is the peak power at a state of charge(SOC) of an aged cell and P₀(SOC) is the peak power at a state of chargeof a freshly manufactured and tested cell at the same state of charge(SOC); optionally a state of charge of 50% is used in determination ofSOH, though other states of charge are optionally used as well. Thefollowing references, hereby incorporated by reference, disclose methodsfor estimating, calculating or measuring a state of health of anelectrochemical cell: Ng et al., Applied Energy 86 (2009) 1506-1511;Remmlinger et al., J. Power Sources 196 (2011) 5357-5363; Andre et al.,Engineering Applications of Artificial Intelligence 26 (2013) 951-961;Lin et al., IEEE Transactions on Industrial Informatics, 9:2 (2013)679-685; Eddahech et al., Electrical Power and Energy Systems 42 (2012)487-494.

In embodiments, the state of safety (SOS) of the electrochemical cellrefers to the likelihood or probability of the electrochemical cell toundergo a thermal runaway. In embodiments, one useful metric fordetermination of SOS is the onset temperature of a thermal event withinthe electrochemical cell at a defined state of charge. In embodiments,the lower the onset temperature, such as that measured by a thermalanalysis method including calorimetric methods, differential thermalanalysis (DTA) methods and differential scanning calorimetric methods(DSC), the higher the thermal runaway risk and thus the lower the SOS.In embodiments, the cycle number of the electrochemical cell refers to anumber of charge or discharge cycles the electrochemical cell hasexperienced, for example the number of full charge or discharge cycles,the number of partial charge or discharge cycles or combinationsthereof.

In embodiments, devices of this aspect analyze a history of one or moreelectrochemical cells in order to determine a state of health or a stateof safety of the electrochemical cell. Useful histories ofelectrochemical cells include, but are not limited to, as an opencircuit voltage history, a temperature history, a state of chargehistory, a thermodynamic parameter history, a cycle number history. Asused herein, the term “history” refers to previous measurements,estimates or analyses of conditions or events of an electrochemical cellmade over a time period. In embodiments, a state of health of anelectrochemical cell is determined by measurement of a peak power of theelectrochemical cell, such as at a specified state of health. In oneembodiment, the electrochemical cell under consideration is brought to adefined state of charge and discharged at a fast increasing power (P=UI,U=voltage, 1=current). Optionally, peak power is defined as the highestpower the cell can sustain for a short period of time, for example overa fraction of a second to a few seconds. In embodiments, a peak powermeasurement is not reversible and may itself adversely affect the cell'sstate of health. In embodiments, a state of safety of an electrochemicalcell is determined through calorimetric methods, such as differentialscanning calorimetry (DSC) and accelerated rate calorimetry (ARC), bydetermining a temperature one set, total heat and self-heating rates ofprocesses within an electrochemical cell at a defined initial state ofcharge.

In a specific embodiment, a device of this aspect determines an entropy,a change in entropy or a differential entropy of the electrochemicalcell and compares the determined entropy, change in entropy ordifferential entropy with a reference entropy, a reference change inentropy or a reference differential entropy and disables charging ordischarging of the electrochemical cell when the determined entropy,change in entropy, or differential entropy is different from thereference entropy, reference change in entropy or reference differentialentropy. In embodiments, the reference entropy, reference change inentropy or reference differential entropy is an entropy, change inentropy or differential entropy of a reference electrochemical cell,such as an electrochemical cell having a preselected state of charge, apreselected state of safety, a preselected state of health or anycombination of these. In embodiments, the electrochemical cell isdisabled from charging or discharging when the determined entropy,change in entropy, or differential entropy is greater than the referenceentropy, reference change in entropy or reference differential entropyor less than the reference entropy, reference change in entropy orreference differential entropy. In an embodiment, a device of thisaspect determines a temperature of the electrochemical cell and comparesthe determined temperature with a reference temperature and disablescharging or discharging said electrochemical cell when the determinedtemperature is greater than the reference temperature.

In embodiments, devices of this aspect comprise one or more integratedcircuits or one or more integrated circuit components. For example, inone embodiment, the integrated circuit comprises a field programmablegate array. In an embodiment, for example, the integrated circuitcomprises an application-specific integrated circuit. Optionally, acircuit component of an integrated circuit comprises a fieldprogrammable gate array or an application-specific circuit. For example,in embodiments, a circuit for determining a thermodynamic parameter ofthe electrochemical cell comprises a field programmable gate array or anapplication-specific integrated circuit.

In another aspect, the present invention provides methods, includingmethods of determining a condition of an electrochemical cell andmethods of determining a parameter of an electrochemical cell. Inembodiments, methods of this aspect provide ways for determining statesof health of an electrochemical cell, for determining a state of chargeof an electrochemical cell, determining a state of safety of anelectrochemical cell, for determining states of safety of anelectrochemical cell, for determining a cycle number of anelectrochemical cell, determining a composition of an electrochemicalcell, determining a change in a phase of one or more components of anelectrochemical cell, and for determining a thermodynamic parameter ofan electrochemical cell, such as a change in entropy (ΔS), a change inenthalpy (ΔH) and a change in free energy (ΔG).

In an embodiment, a method of this aspect comprises the steps of:providing an integrated circuit comprising: a voltage monitoring circuitfor measuring a plurality of open circuit voltages of theelectrochemical cell, the plurality of open circuit voltages generatedupon charging or discharging the electrochemical cell or stoppingcharging or discharging the electrochemical cell, a temperaturemonitoring circuit for measuring a plurality of temperatures of theelectrochemical cell, the plurality of temperatures generated uponcharging or discharging the electrochemical cell or stopping charging ordischarging the electrochemical cell, and a circuit for determining athermodynamic parameter of the electrochemical cell, wherein thethermodynamic parameter is one or more of a change in entropy of theelectrochemical cell, a change in enthalpy of the electrochemical celland a change in free energy of the electrochemical cell, the circuit fordetermining a thermodynamic parameter positioned in electrical or datacommunication with the temperature monitoring circuit to receivetemperature measurements from the temperature monitoring circuit andpositioned in electrical or data communication with the voltagemonitoring circuit to receive open circuit voltage measurements from thevoltage monitoring circuit; generating the plurality of open circuitvoltages of the electrochemical cell, the plurality of temperatures ofthe electrochemical cell or both the plurality of open circuit voltagesof the electrochemical cell and the plurality of temperatures of theelectrochemical cell; and determining a first thermodynamic parameter ofthe electrochemical cell using the integrated circuit.

Optionally, a generating step of a method of this aspect comprisescharging or discharging the electrochemical cell. Optionally, one ormore of a temperature of the electrochemical cell and an open circuitvoltage of the electrochemical cell changes during the charging ordischarging. In this way, embodiments of this aspect can utilize thenatural temperature and open circuit voltage changes associated withcharging or discharging the electrochemical cell for determination of aparameter or condition of the electrochemical cell.

Optionally, a generating step of a method of this aspect comprisesstopping a charging or a discharging of the electrochemical cell.Optionally, one or more of a temperature of the electrochemical cell andan open circuit voltage of the electrochemical cell changes afterstopping the charging or the discharging. Here, embodiments of thisaspect can utilize the natural changes in temperature and open circuitvoltage that occur as an electrochemical cell relaxes back towardsambient temperature after being heated during charging or dischargingfor determination of a parameter or condition of the electrochemicalcell.

In embodiments, methods of this aspect further comprise a step ofcomparing the first thermodynamic parameter with one or more referencethermodynamic parameters for a reference electrochemical cell. In aspecific embodiment, a cell chemistry of the reference electrochemicalcell is identical to a cell chemistry of the electrochemical cell. Inembodiments, methods comprising steps of comparing thermodynamicparameters are useful, for example, because they permit thoroughcharacterization of an reference electrochemical cell under carefullycontrolled conditions in order to provide useful reference measurementsfor later comparison with an electrochemical cell as it is being used,for example in an automotive or portable electronic device application.By comparing a thermodynamic parameter measured for an electrochemicalcell as it is being used with reference thermodynamic parameters for areference electrochemical cell, insights into a condition of theelectrochemical cell can be obtained. For example, method embodimentsincorporating comparison of thermodynamic parameters permit estimationor determination of an electrochemical cell's state of health, state ofsafety, cycle number, and other characteristics of cell aging.

In one embodiment, for example, the step of determining a firstthermodynamic parameter comprises determining a change in entropy forthe electrochemical cell at a first open circuit voltage. Optionally, amethod of this aspect further comprises a step of determining a secondthermodynamic parameter of the electrochemical cell using the integratedcircuit. Optionally, a method of this aspect further comprises a step ofcomparing the second thermodynamic parameter with one or more referencethermodynamic parameters for a reference electrochemical cell. In anembodiment, for example, the step of determining a second thermodynamicparameter comprises determining a change in entropy for theelectrochemical cell at a second open circuit voltage.

Optionally, a step of comparing the first thermodynamic parameter withone or more reference thermodynamic parameters comprises interpolatingbetween points in an array of reference thermodynamic parameters or in alook-up table of reference thermodynamic parameters. As described above,useful reference thermodynamic parameters or in a look-up table ofreference thermodynamic parameters include values determined for areference electrochemical cell. In an embodiment, the step of comparingthe first thermodynamic parameter with one or more referencethermodynamic parameters comprises determining a condition of theelectrochemical cell based on the comparison.

In an exemplary embodiment, the step of determining a firstthermodynamic parameter of the electrochemical cell comprises the stepsof: charging or discharging the electrochemical cell to a first opencircuit voltage value; stopping the charging or discharging; measuringopen circuit voltages of the electrochemical cell as a function of timeusing the integrated circuit; and measuring temperatures of theelectrochemical cell as a function of time using the integrated circuit.Optionally, the step of determining a first thermodynamic parameter forthe electrochemical cell further comprises computing a linear regressionof open circuit voltage measurements versus temperature measurements. Inan embodiment, the measured open circuit voltages of the electrochemicalcell provide values for changes in free energy of the electrochemicalcell, wherein an intercept of the linear regression provides values forchanges in enthalpy of the electrochemical cell and wherein a slope ofthe linear regression provides values for changes in entropy of theelectrochemical cell.

As described previously with reference to devices of the invention, somemethod embodiments do not comprise controlling a temperature of theelectrochemical cell using a temperature controller, a heater, a cooleror any combination of these.

In embodiments, another method of this aspect comprises the steps of:providing a reference array of values comprising thermodynamic parametervalues for a reference electrochemical and cell condition values for thereference electrochemical cell; determining a thermodynamic parameterfor the electrochemical cell; and determining the condition of theelectrochemical cell using the reference array of values, wherein thecondition of the electrochemical cell corresponds to a cell condition ofthe reference electrochemical cell for a reference thermodynamic valueequal to the determined thermodynamic parameter for the electrochemicalcell.

Optionally, the array of values further comprises open circuit voltagevalues for the reference electrochemical cell, as described above. In aspecific embodiment, the array of values comprises two or more opencircuit voltage values, a plurality of thermodynamic parameter valuesfor each of the two or more open circuit voltage values and one or morecell condition values for each of the two or more open circuit voltagevalues and the plurality of thermodynamic parameter values. Optionally,the step of determining the condition of the electrochemical cellcomprises interpolating between values of the array of values.

In embodiments, methods of this aspect advantageously determine one ormore conditions of an electrochemical cell including a state of healthof the electrochemical cell, a state of charge of the electrochemicalcell, a state of safety of the electrochemical cell and a cycle numberof the electrochemical cell. In a specific embodiment, cell conditionvalues in an array of values comprises one or more of a state of healthof the reference electrochemical cell, a state of charge of thereference electrochemical cell, a state of safety of the referenceelectrochemical cell and a cycle number of the reference electrochemicalcell. Optionally, the array of values comprises values for changes inentropy of the reference electrochemical cell at two or more opencircuit voltages.

In specific embodiments, the thermodynamic parameter values for anelectrochemical cell, such as a reference electrochemical cell, areobtained by a method comprising the steps of: controlling a compositionof the reference electrochemical cell to establish a plurality ofreference electrochemical cell compositions; controlling a temperatureof the reference electrochemical cell to establish a plurality ofelectrochemical cell compositions for each of the plurality of referenceelectrochemical cell compositions; measuring open circuit voltages ofthe reference electrochemical cell for each of the plurality ofreference electrochemical cell compositions and the referenceelectrochemical cell temperatures. Such methods are useful, as describedabove, for carefully and thoroughly characterizing an electrochemicalcell, such as a reference electrochemical cell, and particularly fordeveloping multiple arrays of values for a variety of electrochemicalcell chemistries. Optionally, the thermodynamic parameter values for anelectrochemical cell, such as a reference electrochemical cell, areobtained by a method further comprising a step of computing a linearregression of open circuit voltage measurements of the referenceelectrochemical cell versus temperature measurements of the referenceelectrochemical cell. Optionally, the measured open circuit voltages ofthe electrochemical cell provide values for changes in free energy ofthe electrochemical cell, wherein an intercept of the linear regressionprovides values for changes in enthalpy of the electrochemical cell andwherein a slope of the linear regression provides values for changes inentropy of the electrochemical cell.

In a specific embodiment, the step of determining a thermodynamicparameter for the electrochemical cell comprises the steps of: chargingor discharging the electrochemical cell to a first open circuit voltagevalue; stopping the charging or discharging; measuring open circuitvoltages of the electrochemical cell as a function of time; andmeasuring temperatures of the electrochemical cell as a function oftime. Optionally, the step of determining a thermodynamic parameter forthe electrochemical cell further comprises computing a linear regressionof open circuit voltage measurements of the electrochemical cell versustemperature measurements of the electrochemical cell. Optionally, themeasured open circuit voltages of the electrochemical cell providevalues for changes in free energy of the electrochemical cell, whereinan intercept of the linear regression provides values for changes inenthalpy of the electrochemical cell and wherein a slope of the linearregression provides values for changes in entropy of the electrochemicalcell.

In an exemplary embodiment, the step of determining a thermodynamicparameter for the electrochemical cell is performed using an integratedcircuit comprising: a voltage monitoring circuit for measuring aplurality of open circuit voltages of the electrochemical cell, theplurality of open circuit voltages generated upon charging ordischarging the electrochemical cell or stopping charging or dischargingthe electrochemical cell; a temperature monitoring circuit for measuringa plurality of temperatures of the electrochemical cell, the pluralityof temperatures generated upon charging or discharging theelectrochemical cell or stopping charging or discharging theelectrochemical cell; and a circuit for determining a thermodynamicparameter of the electrochemical cell, wherein the thermodynamicparameter is one or more of a change in entropy of the electrochemicalcell, a change in enthalpy of the electrochemical cell and a change infree energy of the electrochemical cell, the circuit for determining athermodynamic parameter positioned in electrical or data communicationwith the temperature monitoring circuit to receive temperaturemeasurements from the temperature monitoring circuit and positioned inelectrical or data communication with the voltage monitoring circuit toreceive open circuit voltage measurements from the voltage monitoringcircuit.

In a specific embodiment, the step of determining a thermodynamicparameter for the electrochemical cell does not comprise controlling atemperature of the electrochemical cell using a temperature controller,a heater, a cooler or any combination of these. Optionally, the step ofdetermining a thermodynamic parameter for the electrochemical cellcomprises generating a plurality of open circuit voltages of theelectrochemical cell, a plurality of temperatures of the electrochemicalcell or both a plurality of open circuit voltages of the electrochemicalcell and a plurality of temperatures of the electrochemical cell.

Optionally, the generating step comprises charging or discharging theelectrochemical cell; wherein a temperature of the electrochemical cellchanges during the charging or discharging, wherein an open circuitvoltage of the electrochemical cell changes during the charging ordischarging or wherein both a temperature of the electrochemical celland an open circuit voltage of the electrochemical cell change duringthe charging or discharging. Optionally, the generating step comprisesstopping a charging or a discharging of the electrochemical cell;wherein a temperature of the electrochemical cell changes after stoppingthe charging or the discharging, wherein an open circuit voltage of theelectrochemical cell changes after stopping the charging or thedischarging or wherein both a temperature of the electrochemical celland an open circuit voltage of the electrochemical cell change afterstopping the charging or the discharging.

In another aspect provided are methods for safely operating anelectrochemical cell. A specific embodiment of this aspect comprises thesteps of: providing an electrochemical cell; providing an entropymonitoring circuit for monitoring an entropy of the electrochemicalcell, the circuit positioned in electrical communication with theelectrochemical cell; determining an entropy of the electrochemical cellusing the entropy monitoring circuit; comparing the determined entropyof the electrochemical cell with a reference entropy; and disabling theelectrochemical cell from charging or discharging when the determinedentropy of the electrochemical cell is different from the referenceentropy. In embodiments, methods of this aspect provide for safeoperation and monitoring of electrochemical cells, such as to preventelectrochemical cells from operating under conditions in which thermalrunaway of the electrochemical cell is likely to take place. Inembodiments, methods of this aspect provide a way to disable or bypasselectrochemical cells which are determined to be unfit for safeoperation, thereby preventing further increasing the likelihood that theelectrochemical cell will undergo thermal runaway.

Optionally, the reference entropy is an entropy of a referenceelectrochemical cell having a preselected state of safety, a preselectedstate of charge, a preselected state of health or any combination ofthese, such as a reference electrochemical cell that is approaching theend of its useful life and should be removed from operation to preventunsafe conditions. In a specific embodiment, the disabling stepcomprises actuating a switch, relay or transistor in electricalcommunication with an electrode of the electrochemical cell, therebydisabling charging or discharging the electrochemical cell. Optionally,the determining step comprises determining a change in entropy of theelectrochemical cell. Optionally, the comparing step comprises comparingthe change in entropy of the electrochemical cell with a referencechange in entropy. Optionally, the disabling step comprises disablingthe electrochemical cell from charging or discharging when thedetermined change in entropy of the electrochemical cell is greater thanthe reference change in entropy. Optionally, the determining stepcomprises determining a differential entropy of the electrochemicalcell. Optionally, the comparing step comprises comparing thedifferential entropy of the electrochemical cell with a referencedifferential entropy. Optionally, the disabling step comprises disablingthe electrochemical cell from charging or discharging when thedetermined differential entropy of the electrochemical cell is greaterthan the reference differential entropy. In a specific embodiment, thestep disabling step disables the electrochemical cell from charging ordischarging with the determined entropy is greater than the referenceentropy or less than the reference entropy.

In another embodiment, a method of this aspect further comprises thesteps of: monitoring a temperature of the electrochemical cell;comparing the temperature of the electrochemical cell with a referencetemperature; and disabling the electrochemical cell from charging ordischarging when the temperature of the electrochemical cell is greaterthan the reference temperature. Optionally, these embodiments provideanother means for ensuring safe operation of an electrochemical cell orfor determining whether an electrochemical cell has begun thermalrunaway or will later undergo thermal runaway if the cell is continuedin operation. Optionally, the reference temperature is a temperature ofa reference electrochemical cell having a preselected state of safety, apreselected state of charge, a preselected state of health or anycombination of these. Optionally, the disabling step comprises actuatinga switch, relay or transistor in electrical communication with anelectrode of the electrochemical cell, thereby disabling charging ordischarging the electrochemical cell.

In an exemplary embodiment, methods of this aspect utilize devicesdescribed herein for monitoring an entropy of an electrochemical cell.In a specific embodiment, the entropy monitoring circuit comprises anintegrated circuit comprising: a voltage monitoring circuit formeasuring a plurality of open circuit voltages of the electrochemicalcell, the plurality of open circuit voltages generated upon charging ordischarging the electrochemical cell or stopping charging or dischargingthe electrochemical cell; a temperature monitoring circuit for measuringa plurality of temperatures of the electrochemical cell, the pluralityof temperatures generated upon charging or discharging theelectrochemical cell or stopping charging or discharging theelectrochemical cell; a current monitoring circuit for measuring acharging current of the electrochemical cell or a discharging current ofthe electrochemical cell; and a circuit for determining a thermodynamicparameter of the electrochemical cell, wherein the thermodynamicparameter is one or more of a change in entropy of the electrochemicalcell, a change in enthalpy of the electrochemical cell and a change infree energy of the electrochemical cell, the circuit for determining athermodynamic parameter positioned in electrical or data communicationwith the temperature monitoring circuit to receive temperaturemeasurements from the temperature monitoring circuit, positioned inelectrical or data communication with the voltage monitoring circuit toreceive open circuit voltage measurements from the voltage monitoringcircuit and positioned in electrical or data communication with thecurrent monitoring circuit to receive current measurements from thecurrent monitoring circuit or to provide thermodynamics parameters tothe current monitoring circuit.

In the context of this description, the term “thermodynamicallystabilized conditions” refers to experimental conditions whereinmeasured open circuit voltages approximate equilibrium cell voltage suchthat the measurements can be used to determine thermodynamic parametersand materials properties with accuracies such that these parameters maybe used to evaluate the electrochemical, materials and performanceattributes of the electrodes and/or electrochemical cell. Measurement ofopen circuit voltages for thermodynamically stabilized conditionsenables determination of state functions such as the Gibbs free energy,enthalpy and entropy of electrode/electrochemical cell reactions. It isintended that thermodynamically stabilized conditions include somedeviations from absolute equilibrium conditions. In some embodimentsopen circuit voltages for thermodynamically stabilized conditionsdeviate from true equilibrium voltages by less than 1 mV and preferably,for some embodiments, conditions deviate from true equilibrium voltagesby less than 0.1 mV. Under some experimental conditions of the presentinvention, the open circuit voltages are nearly an exact measure of thedifference in Gibbs free energy of Li in the anode and cathode and anyobserved deviations originate from limitations in the measurementtechniques employed during analysis. The ability to accurately identifyopen circuit voltage measurements reflecting thermodynamicallystabilized conditions is useful for providing measurements of opencircuit voltage, temperature and composition that may be used forcharacterization of important thermodynamic, electrochemical andmaterials properties of the electrodes analyzed.

In some embodiments, the expression “electrochemical cell” refers to adevice comprising of three major active materials:

anode: is typically the electrode where an oxidation takes place.Oxidation is a loss of electron and can be schematized as:R_(a)→O_(a)+n_(a)e, wherein R_(a) is the reduced form and O_(a) is theoxidized form of a chemical specie or used for the anode material. Itcomprises a neutral or positively charged (cation) or negatively charged(anion), n_(a)=number of electron moles exchanged in the anode reactionper R_(a) mole. The anode is the negative pole of the cell duringdischarge;

cathode: is typically the electrode where a reduction (electron gain)takes place. The reaction is the reverse of the previous one, i.e.O_(c)+n_(c)e→R_(c), wherein O_(c) is the oxidized form and R_(c) is thereduced form of a chemical specie or used for the cathode material. Itcomprises a neutral or positively charged (cation) or negatively charged(anion), n_(c)=number of electron moles exchanged in the anode reactionper O_(c) mole. The cathode is the positive pole of the cell duringdischarge; and

electrolyte: is an ionically conductive material, which role is toprovide anions and cations needed for the electrode reactions to beachieved. It usually comprises a solvent medium and a solute materialsuch as a salt, an acid or a base. In some cases, the electrolytechanges composition a result of the cell's charge and discharge (see,lead-acid batteries for example where sulfuric acid is consumed duringdischarge: Pb+PbO₂+2H₂SO₄→2PbSO₄+2H₂O)

As used herein, the expressions “electrochemical cell composition” or“composition of an electrochemical cell” are used synonymously and referto compositions and/or physical states of active materials comprisingthe electrochemical cell (i.e., electrodes such as cathode and anode,and the electrolyte). Accordingly, in some embodiments electrochemicalcell composition refers to surface and/or bulk compositions of cathodeand anode materials, the composition of the electrolyte or anycombination of these). In some embodiments of the present invention, theexpression “composition of an electrochemical cell” refers to the stateof charge of the electrochemical cell or any component thereof (e.g.active material such as electrodes or electrolyte).

Examples of electrochemical cells useful in the present inventioninclude, but are not limited to, batteries (primary and secondary) andfuel cells. While the above anode and cathode reactions arecharacteristic of electrode processes in batteries and fuel cells andinvolve electron transfer between the electrolyte and the electrode in aso called faradaic process (or Redox process), there are othernon-faradaic processes that allow for electrical charges storage at theelectrode surface without a charge transfer or a Redox process.

Examples of electrochemical cells useful in the present inventioninclude, but are not limited to, electrochemical double layer capacitors(EDLC) and electrochemical double layer supercapacitors. In anelectrochemical double layer capacitor EDLC (or supercapacitor), ananion A⁻or a cation C⁺ is stored on the electrode surface owing toaccumulation of electrons (e⁻) or electron holes (h⁺) at theelectrode-electrolyte interface to balance the adsorbed charge speciesand form neutral species in a double layer structure: (A⁻, h⁺) and (C⁺,e⁻). During charge and discharge the anions and/or cations are adsorbedor desorbed from the surface, which causes an electric current flow inthe external circuit (charger or load) to balance for surface charges.

Hybrid supercapacitors are an intermediary category of electrical powersources between batteries and EDLC. They are hybrid because they combinetwo electrodes, one is a faradaic electrode like in a battery, and theother is a non-faradaic (capacitive) electrode like in an EDLC.

Batteries, fuel cells and EDLC are polarized systems in that the voltageof the anode and the cathode are different. During discharge, thecathode has the higher voltage V⁺; therefore it is the positive pole,whereas the anode bears the lower voltage V⁻and is the negative pole.The difference in voltage U=V⁺−V⁻depends on different parameters, themost important are:

State of charge: (SOC) of each electrode. SOC is usually given in % ofthe total charge theoretically stored in the anode (Q_(th)(an) or thecathode (Q_(th)(ca); Density of discharge current (i): Under zerocurrent, U_(i=0) is the open-circuit voltage, which with time tends toan equilibrium value U_(∞) fixed by SOC and temperature; Temperature;State of health (SOH) of the system components: for anode, cathode andelectrolyte the SOH varies with the system ‘history’, such as for themost common charge/discharge cycles, overcharge and overdischarge andthermal aging. Since a battery, a fuel cell and an EDLC function in a‘series’ mode, any degradation of one of the active components: anode,cathode and electrolyte, will affect the cell's SOH.

With changing SOC, the electrodes surface or bulk composition changesand in some cases the electrolyte composition changes too. These changesin electrode surface and/or bulk composition and/or electrolytecomposition establish, at least in part, the composition of theelectrochemical cell (i.e. electrochemical cell composition) asdescribed herein. Change in electrode composition is especially relevantfor battery systems wherein electrolyte is consumed (e.g., lead acid,NiCd and Zn-silver batteries (See: reactions below)) and in normal orhybrid EDLCs.

A. Reactions for Lead Acid Battery

Negative Electrode:

Positive Electrode:

Overall Reaction:

B. Reactions for Nickel-Cadmium System

C. Reactions for Silver-Zinc, Silver-Cadmium and Silver-Iron Systems

The present measurement system is capable of measuring thermodynamicfunctions of a half- or a full-cell at different SOC of the anode,cathode and electrolyte.

As used herein the expression “composition of an electrochemical cell”refers generally to bulk compositions and/or surface compositions ofcomponents of an electrochemical cell. In some embodiments, compositionof an electrochemical cell refers to the composition of electrodes ofthe electrochemical cell, such as compositions of electrodes (e.g.,cathode and/or anode electrodes) of the electrochemical cell. Inembodiments wherein the electrode(s) is an intercalating electrode, thecomposition of an electrochemical cell may refer to the stoichiometry ofthe intercalating electrode materials with respect to the amount ofintercalant physically associated with the electrode, the absoluteamount of intercalant physically associated with the electrode, or theconcentration of intercalant physically associated with the electrode.In some embodiments, the expression “composition of the electrochemicalcell” refers to the composition of the electrolyte (e.g., theconcentration(s) of components (ionic and/or nonionic) of theelectrolyte). In some useful embodiments of the present invention, theexpression “composition of an electrochemical cell” refers to the stateof charge of the electrochemical cell or any component thereof, such asthe state of charge of an electrode (cathode, anode, working, counteretc.) or combination of electrodes.

Coulometry is a technique useful in the present invention for measuringand/or selecting the electrochemical cell composition by establishingand/or determining the SOC of an electrochemical cell. In someembodiments, therefore, the composition controller comprises acoulometer. For example, let i(t) be the current intensity in the cellat time T. The total amount of charge Q(t) at time τ is given by thetime integration of i(t):

$\begin{matrix}{{Q(\tau)} = {\int_{0}^{\tau}{{i(t)}\ {t}}}} & (1)\end{matrix}$

The SOC of anode (an), cathode (cat) and electrolyte (elec) is given inas:

$\begin{matrix}{{{SOC}( {{an},{cat},{{elec}.}} )} = {100\frac{Q(t)}{Q_{th}( {{an},{cat},{{elec}.}} )}}} & (2)\end{matrix}$

The SOC of the full cell is fixed by that of the limiting component,anode, cathode or electrolyte:

SOC(full cell)=inf(SOC(an),SOC(cat),SOC(elec))  (3)

(the ‘inf’ function refers to the lowest value of a group ofparameters). The electrochemical techniques for acquiring i(t) include,but are not limited to, the following:

Galvanostatic method: here the applied current or current density isconstant i(t)=I. The amount of electricity passed is thereforeproportional to time: Q(t)=It. Usually the electrode or cell voltage isplotted versus time, a technique called chronopotentiometry.

Constant voltage: applying a constant voltage different from thethermodynamic OCV will cause a current i(t) to flow in the cell. Thelatter is recorded versus time, a technique called chronoamperometry. Avariant of this method is the ‘voltage step’ method, where a series ofvoltage steps U_(n) (n=step number) are applied usually with a constantincrement δU (U_(n)=U₀±n δU). At each step, the current is recorded andintegrated.

Potentio-dynamic methods such as linear sweep voltammetry and cyclicvoltammetry: in this method the voltage is driven between two limitvalues U_(up) and U_(low) at a constant pace (U(t)=Uo±kt, k=constant,U_(low)<U(t)<U_(up)). The current response i(t) is recorded andgenerally plotted against U(t).

Discharge under constant load: the cell is connected to a resistance andthe current is recorded versus time.

By proper selection of the compositions, design and/or experimentalconditions of the electrochemical cell, the measurement system of thepresent invention can probe the materials properties, SOH,thermodynamics and/or materials properties of a single component of theelectrochemical cell, such as a selected electrode (cathode or anode) orthe electrolyte, and chemical reactions occurring on or in a singlecomponent of the electrochemical cell. Selection of such electrochemicalcell and measurement system configurations are beneficial for using thepresent measuring system to generate useful information (thermodynamic,composition, physical properties etc.) relating to a single activecomponent of an electrochemical cell and chemical reactions thereof. Forexample, by choice of an electrochemical cell having a first electrode(e.g. counter electrode) having a chemical potential that is independentof the state of charge of the electrochemical cell, the system of thepresent invention is capable of generating measurements of open circuitvoltage for thermodynamically stabilized conditions for differentcompositions and/or states of charge of the second electrode (e.g.working electrode). In one embodiment, for example, use of a firstelectrode (e.g. counter electrode) comprising a pure electrode material(e.g., a lithium, cadmium or zinc pure metal electrode) is useful forproviding open circuit voltage measurements that principally reflect thestate of charge, composition and/or chemical reactions of the secondelectrode (e.g. working electrode). More generally, however, systems ofthe present invention employing a reference electrode (i.e., a thirdelectrode), in addition to first and second electrodes, may be used toprovide measurements of open circuit voltage or thermodynamicparameters, for example, as a function of the composition and/or stateof charge (SOC) of a selected electrode (e.g., cathode or anode). Inthese embodiments, the incorporation of a reference electrode (i.e. athird electrode), therefore, allows accurate measurements of opencircuit voltage for thermodynamically stabilized conditions fordifferent compositions, temperatures and chemical reactions of aselected electrode of the electrochemical cell. Use of such systemconfigurations is highly beneficial for providing thermodynamic andother useful information that principally reflects the chemistry,physical properties, thermodynamics and structure of a singleelectrochemical cell component. For example, use of a referenceelectrode or selection of an electrode having a chemical potential thatis independent of the state of charge of the electrochemical cell allowsthermodynamic state functions (ΔH, ΔS and ΔG) to be determined thatcorrespond to a single electrode reaction. Such information is usefulfor the structural, thermodynamic and chemical characterization ofelectrochemical cell components, and may serve the basis for testing andquality control methods for evaluating components of electrochemicalcells.

Open circuit voltage analyzers and voltage monitoring circuits of thepresent invention are capable of determining open circuit voltages, forexample, that correspond to thermodynamically stabilized conditions orapproximately thermodynamically stabilized conditions. In someembodiments, an open circuit voltage analyzer or voltage monitoringcircuit is also capable of open circuit voltage data acquisition and, ofoptionally providing analysis of the data generated by the measurementsystem including calculating thermodynamic state functions, such aschanges in entropy and enthalpy, and generating plots of thermodynamicstate functions versus open circuit voltage or electrochemical cellcomposition useful for characterizing electrochemical cells andelectrode materials. Useful open circuit analyzers and voltagemonitoring circuits include, but are not limited to, those comprisingprocessors capable of executing algorithms that utilize open circuitmeasurements as a function of time to identify open circuit voltagesthat correspond to thermodynamically stabilized conditions orapproximately thermodynamically stabilized conditions. In an embodiment,an open circuit voltage analyzer or voltage monitoring circuit iscapable of calculating observed rates of change in open circuit voltageper unit time (ΔOCV/Δt)_(observed) for electrochemical cell as afunction of time. For example, an open circuit voltage analyzer orvoltage monitoring circuit is optionally configured such that itdirectly or indirectly monitors open circuit voltage and calculatesobserved rates of change in open circuit voltage per unit time. For eachobserved rate of change in open circuit voltage per unit time, theabsolute value of the observed rates of change in open circuit voltageper unit time is optionally compared to a threshold rate of change inopen circuit voltage per unit time (ΔOCV/Δt)_(threshold). An opencircuit voltage analyzer or voltage monitoring circuit determines thatan open circuit voltage is equal to the open circuit voltage of theelectrochemical cell for thermochemically stabilized conditions for theselected electrochemical cell temperature and composition combinationwhen the absolute value of the observed rate of change in open circuitvoltage per unit time is equal to or less than the threshold rate ofchange in open circuit voltage per unit time:

${( \frac{\Delta \; {OCV}}{\Delta \; t} )_{observed}} \leq {( \frac{\Delta \; {OCV}}{\Delta \; t} )_{Threshold}.}$

In exemplary embodiments, the threshold rate of change in open circuitvoltage as a function of time is equal to or less than 1 mV h⁻¹(millivolt per hour) and preferably for some applications the thresholdrate of change in open circuit voltage as a function of time is equal toor less than 0.3 mV h⁻¹, and more preferably for some applications thethreshold rate of change in open circuit voltage as a function of timeis equal to or less than 0.1 mV h⁻¹.

Optionally, an open circuit voltage analyzer or voltage monitoringcircuit monitors the open circuit voltage of an electrochemical cell fora set period of time, for example a time period smaller than thatrequired for the electrochemical cell to relax to thermochemicallystabilized conditions. The open circuit voltage analyzer or voltagemonitoring circuit then determines an exponential or other growth ordecay rate in order to compute the open circuit voltage forthermochemically stabilized conditions from the growth or decay rate anda measured open circuit voltage for non-thermochemically stabilizedconditions. Such a process permits determination of an open circuitvoltage for thermochemically stabilized conditions even thoughthermochemically stabilized conditions are not directly measured, forexample by extrapolating the open circuit voltage trend without havingto wait for equilibrium values to be reached. For example, in oneembodiment, a mathematical model is used for determination ofequilibrium values by extrapolation. D. M. Bernardi et al., J. PowerSources 196 (2011) 412-427, herein incorporated by reference in itsentirety, provides example methods for determination of equilibriumvalues by extrapolation

In one embodiment, for example, the open circuit voltage analyzer,voltage monitoring circuit or other system component measures opencircuit voltages at various times and uses this information torepeatedly (periodically or aperidocially) calculate observed rates ofchange in open circuit voltage per unit time. When the observed rate ofchange (ΔOCV/Δt)_(observed) calculated is equal to or less than thethreshold rate of change (ΔOCV/Δt)_(threshold), the open circuit voltageanalyzer or voltage monitoring circuit may determine that the mostrecent open circuit voltage measurement is equal to the open circuitvoltage for thermochemically stabilized conditions, may determine thenext open circuit voltage to be measured is equal to the open circuitvoltage for thermochemically stabilized conditions, or may calculate atime averaged valued of open circuit voltage corresponding toexperimental conditions when|(ΔOCV/Δt)_(observed)|≦(ΔOCV/Δt)_(threshold).

A significant capability of the present system is that it provides ameans of establishing electrochemical cell conditions and collectingvoltage, time and temperature measurements with the enhanced accuracyrequired to enable accurate thermodynamic analysis. Selection of acombination of a means for measuring open circuit voltage accurate towithin about 1 mV and a temperature sensor capable of sensingelectrochemical cell temperatures to within about 0.1 degrees Kelvin,for example, provides a number of benefits. For example, thiscombination of system component performance attributes providesmeasurements accurate enough to determine a range of importantthermodynamic parameters and materials properties of many electrodematerials and/or electrochemical energy conversion and storage systems.Further, these performance attributes enable thermodynamic statefunctions, such as the Gibbs free energy, enthalpy and entropy ofelectrode/electrochemical cell reactions, to be determined usingmeasurements corresponding to a relatively narrow range of temperatures(e.g. less than or equal to about 10 degrees Kelvin). For someapplications, confining measurements to a narrow range ofelectrochemical cell temperatures is beneficial for avoiding thermallyactivated phase changes in electrode materials that make thermodynamicanalysis difficult and for avoiding electrochemical cell temperatureswhere self-discharge of the electrochemical cell is significant.

Methods of the present invention may further comprise a number ofanalysis steps wherein measurements of open circuit voltage,electrochemical cell composition, time and/or temperature are used tocharacterize thermodynamics and materials properties of the electrodes,electrolyte and/or electrochemical cell and/or to predictelectrochemical performance parameters for these systems such as energy,energy density, power density, current rate, discharge voltage, capacityand the cycle life.

One method of the present invention, for example, further comprisesanalysis steps of generating plots or computing a linear regression ofthe open circuit voltages of the electrochemical cell versustemperature. In this embodiment, determination of slopes and interceptsfor each of the plots or regressions corresponds to measured changes inentropy (ΔS) and enthalpy (ΔH), respectively, for reactions at theelectrodes for each of the cell compositions. Analysis steps of thisaspect of the present invention may further comprise calculating changesin Gibbs free energy (ΔG) for reactions at the electrodes for each ofthe cell compositions using the determined entropy and enthalpy data.

A method of the present invention, for example, further comprisesanalysis steps of: (i) generating a plot of measured changes in entropy(ΔS) versus electrochemical cell composition and/or (ii) generating aplot of measured changes in enthalpy (ΔH) versus electrochemical cellcomposition; (iii) generating a plot of measured changes in entropy (ΔS)versus open circuit voltage and (iv) generating a plot of changes inentropy (ΔS) versus changes in enthalpy (ΔH). Features in such plots ofΔS or ΔH versus electrochemical cell composition or open circuit voltageare useful for characterizing phase (and changes in phase), morphologyand/or structural defects in electrode materials. Furthermore, suchparametric entropy and enthalpy curves can be used as a ‘fingerprint’for characterizing and/or identifying an electrode (e.g., cathode and ananode) material, an electrolyte and/or an electrochemical cell. As thematerial cycles in the battery, these traces change due to physicaland/or chemical changes occurring in the electrode materials. Thepresent methods, therefore, are useful for evaluating the ‘state ofhealth’ of an electrode material upon heavy cycling or exposing to hightemperatures or to overpotentials (overcharge and overdischarge for acathode and an anode, respectively) or to provide quality controlinformation regarding the presence of defects in electrodes andelectrochemical systems.

Even when the composition of the electrode material is not well known,it is still very useful to plot the ΔS versus the OCV or electrochemicalcell composition to ascertain the materials properties of theelectrodes. The ΔS and the ΔH are functions of the chemical compositionof the electrode material, and parametric plots of ΔS and ΔH versus opencircuit voltage or composition is very sensitive to differences in thecomposition and structures of different materials. Accordingly, theseparametric plots can serve as a “fingerprinting” for different materialsso as to ascertain the identity, composition, structure, defectstructure etc. of electrode materials, even when composition is not wellknown in advance.

Thermodynamic measuring methods and systems of the present inventionenable a broad range of functionalities. In embodiments, methods of thepresent invention comprise a method of predicting one or moreperformance parameter of an electrode and/or electrochemical cellincluding the capacity, specific energy, power, cycle life, cellvoltage, stability, self-discharge or discharge current of theelectrochemical cell. In embodiments, methods of the present inventioncomprise a method of assessing the composition, morphology, phase orphysical state of an electrode(s) or electrochemical cell. Inembodiments, methods of the present invention comprise a method ofidentifying surface, bulk and crystal defect structures in electrodematerials or electrochemical cell. In embodiments, methods of thepresent invention comprise a method of identifying a phase transition inelectrode materials.

In one aspect, the SOH of a battery is related to the SOH of one (or acombination) of three major cell components: anode, cathode andelectrolyte. The thermodynamic functions (ΔG, ΔS and ΔH) of eachelectrode reaction are used as the fingerprint of the correspondingelectrode's SOH. These functions can be plotted versus the ‘electrodecomposition’ or the ‘electrode Potential’ to provide a quantitativecharacterization of the electrochemical cell or any component thereof.

The present invention also provides methods for determining the SOH ofan electrochemical cell, for example an electrochemical cell comprisinga host material. An embodiment of this aspect comprises the steps of:determining a ΔG, ΔS and/or ΔH of the electrochemical cell for aplurality of selected electrochemical cell compositions; determiningstates of charge of the electrochemical cell for each of the pluralityof selected electrochemical cell compositions; identifying the states ofcharge and ΔG, ΔS and/or ΔH corresponding to an event or condition ofthe electrochemical cell; and comparing the ΔG, ΔS and/or ΔHcorresponding to the event or condition of the electrochemical cell toreference ΔG, ΔS and/or ΔH corresponding to the event or condition of areference electrochemical cell.

In specific embodiments, the event or condition includes, but is notlimited to: a 0% charge state of the electrochemical cell, a 100% chargestate of the electrochemical cell, one or more specific partial chargestates of the electrochemical cell and a phase transition taking placewithin the electrochemical cell. For certain embodiments, the selectedelectrochemical cell compositions correspond to compositions of anelectrode of the electrochemical cell, compositions of an electrolyte ofthe electrochemical cell and/or compositions or more than one electrodeof the electrochemical cell. In an exemplary embodiment, the referenceΔG, ΔS and/or ΔH are ΔG, ΔS and/or ΔH for the electrochemical cell at aprevious charge cycle.

The methods and systems of the present invention also are capable ofthermodynamically evaluating virtually any electrochemical system havingan electrode pair including, but not limited to, gas electrodes,electrochemical sensors, catalysis materials, corrosion systems,electro-deposition systems and electrosynthesis systems.

The methods and systems of the present invention also are capable ofthermodynamically evaluating and otherwise analyzing virtually any typeof electrode or any electrode material including, but not limited to,host electrode materials and intercalating electrode materials such ascarbon electrodes, nanostructure metal oxide electrodes andnano-phosphate electrodes.

Without wishing to be bound by any particular theory, there can bediscussion herein of beliefs or understandings of underlying principlesrelating to the invention. It is recognized that regardless of theultimate correctness of any mechanistic explanation or hypothesis, anembodiment of the invention can nonetheless be operative and useful.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 provides a block diagram of an electrochemical thermodynamicmeasurement system (ETMS).

FIG. 2 provides a block diagram of an electrochemical thermodynamicmeasurement system (ETMS) incorporated into a single chip.

FIG. 3 illustrates a block diagram for a electrochemical thermodynamicmeasurement system including temperature control components.

FIG. 4 illustrates an embodiment comprising a circuit for determining athermodynamic parameter.

FIG. 5 illustrates a power switching circuit embodiment.

FIGS. 6A and 6B illustrate voltage converter circuit embodiments.

FIG. 7 illustrates a temperature to voltage converter embodiment

FIG. 8 illustrates a voltage differentiator embodiment.

FIG. 9 illustrates a division circuit embodiment.

FIGS. 10A and 10B illustrate modulation circuit embodiments.

FIGS. 11-14 illustrates open circuit voltage versus temperature dataobtained for four cells in which the temperature of the cells was notcontrolled.

FIG. 15 provides a summary of the analysis results of FIGS. 11-14.

FIG. 16 illustrates data showing a comparison of measurements of opencircuit voltage obtained with and without temperature control.

FIG. 17 illustrates data showing a comparison of measurements of changesin entropy obtained with and without temperature control.

FIG. 18 illustrates data showing a comparison of measurements of changesin enthalpy obtained with and without temperature control.

FIGS. 19 and 20 provide data illustrating the discharge profiles ofcells aged at 60° C. and 70° C., respectively, over a period of 8 weeks.

FIGS. 21A and 21B provide a summary of the discharge characteristicsafter aging at 60° C. and 70° C., respectively.

FIG. 22 provides data illustrating the entropy profiles of lithium ioncells aged at 70° C.

FIG. 23 provides data illustrating the enthalpy profiles of lithium ioncells aged at 70° C.

FIG. 24 provides data illustrating differential entropy profiles oflithium ion cells aged at 70° C.

FIG. 25 provides data illustrating differential enthalpy profiles oflithium ion cells aged at 70° C.

FIG. 26 illustrates data providing the state of health versusdifferential entropy of cells aged at 60° C.

FIG. 27 illustrates data providing the state of health versusdifferential entropy of cells aged at 70° C.

FIG. 28 provides data illustrating the discharge profile of cellsovercharged at different cut-off voltages.

FIG. 29 summarizes the discharge characteristics after overchargingcells to different cut-off voltages.

FIG. 30 provides data showing entropy profiles of electrochemical cellsovercharged to different cut-off voltages.

FIG. 31 provides data showing enthalpy profiles of electrochemical cellsovercharged to different cut-off voltages.

FIG. 32 illustrates data providing the state of health versusdifferential entropy of overcharged cells.

FIG. 33 provides a summary of discharge characteristics of cells aftercycling for a specified number of cycles.

FIG. 34 provides data showing differential entropy profiles of cellsafter cycling.

FIG. 35 provides data showing differential enthalpy profiles of cellsafter cycling.

FIG. 36 illustrates data providing the state of health versusdifferential entropy of cycled cells.

FIG. 37 provides data illustrating the differential entropy profile ofthe fresh and aged cells.

FIG. 38 provides data from accelerating rate calorimetry experimentsshowing the self-heating rate for fresh and aged cells.

FIG. 39 illustrates data showing self-heating peak intensity plotted asa function of differential entropy peak intensity at 5% SOC.

FIG. 40 illustrates data showing self-heating peak intensity as afunction of differential entropy peak intensity at 80% SOC.

FIG. 41 illustrates BA-1000 equipment used to perform thermodynamicsmeasurements; (A) Central unit with a potentiostat/galvanostat, and (B)Coin cells holder (Courtesy of KVI PTE, LTD).

FIG. 42 provides OCP vs. SOC profiles of uncycled (fresh) cells duringcharge.

FIG. 43 provides entropy vs. SOC profiles of uncycled (fresh) cellsduring charge. A1 and A2 data points correspond to onsets of phasetransitions in the graphite anode and C1 to C5 correspond to phasetransition onsets in the LCO cathode.

FIG. 44 provides enthalpy vs. SOC profiles of uncycled (fresh) cellsduring charge. A1 and A2 data points correspond to onsets of phasetransitions in the graphite anode and C1 to C5 correspond to phasetransition onsets in the LCO cathode.

FIG. 45 provides discharge profiles of LiB cells subjected to differentcharge cut-off voltages (COV).

FIG. 46 provides OCP profiles of LiB cells vs. SOC. Cells were subjectedto different COV.

FIG. 47 provides entropy profiles of overcharged LIB cells vs. SOC atdifferent COV.

FIG. 48 provides enthalpy profiles of overcharged LIB cells vs. SOC, atdifferent COV.

FIG. 49 provides entropy profiles of overcharged LIB cells vs. OCP, atdifferent COV.

FIG. 50 provides enthalpy profiles of overcharged LIB cells vs. OCP, atdifferent COV.

FIG. 51 provides a three dimensional (ΔS, ΔH, q_(CL)) plot at 3.87V OCPof LIB overcharged cells, at different COV.

FIG. 52 provides a 2D projected curve on the (ΔS, ΔH) plan at 3.87V OCPof LIB overcharged cells at different COV.

FIG. 53 provides a three dimensional (ΔS, ΔH, q_(CL)) plot at 3.94V OCPof LIB overcharged cells, overcharged cells at different COV.

FIG. 54 provides a 2D projected curve on the (ΔS, ΔH) plan at 3.94V OCPof LIB overcharged cells, overcharged cells at different COV.

FIG. 55A provides discharge profiles of LiB cells subjected to thermalageing at 60° C. for 0-8 weeks. FIG. 55B provides discharge profiles ofLiB cells subjected to thermal ageing at 70° C. for 0-8 weeks

FIG. 56A provides OCP profiles of LIB cells vs. SOC. Cells weresubjected to thermal ageing at 60° C. for 0-8 weeks. FIG. 56B providesOCP profiles of LIB cells vs. SOC. Cells were subjected to thermalageing at 70° C. for 0-8 weeks.

FIG. 57A provides entropy profiles of LIB cells aged at 60° C. vs. SOCfor 0-8 weeks. FIG. 57B provides entropy profiles of LIB cells aged at70° C. vs. SOC for 0-8 weeks.

FIG. 58A provides enthalpy profiles of LIB cells aged at 60° C. vs. SOCfor 0-8 weeks. FIG. 58B provides enthalpy profiles of LIB cells aged at70° C. vs. SOC for 0-8 weeks.

FIG. 59A provides entropy profiles of LIB cells aged at 60° C. vs. OCPfor 0-8 weeks. FIG. 59B provides entropy profiles of LIB cells aged at70° C. vs. OCP for 0-8 weeks.

FIG. 60A provides enthalpy profiles of LIB cells aged at 60° C. vs. OCPfor 0-8 weeks. FIG. 60B provides enthalpy profiles of LIB cells aged at70° C. vs. OCP for 0-8 weeks.

FIG. 61A provides a 3D (ΔS, ΔH, q_(CL)) plot at 3.87V OCP of LIB cellsaged at 60° C. for 0-8 weeks. FIG. 61B provides a 3D (ΔS, ΔH, q_(CL))plot at 3.87V OCP of LIB cells aged at 70° C. for 0-8 weeks.

FIG. 62A provides a 2D projected curve on the (ΔS, ΔH) plan at 3.87V OCPof LIB cells aged at 60° C. for 0-8 weeks. FIG. 62B provides a 2Dprojected curve on the (ΔS, ΔH) plan at 3.87V OCP of LIB cells aged at70° C. for 0-8 weeks.

FIG. 63A provides a 3D (ΔS, ΔH, q_(CL)) plot at 3.94V OCP of LIB cellsaged at 60° C. for 0-8 weeks. FIG. 63B provides a 3D (ΔS, ΔH, q_(CL))plot at 3.94V OCP of LIB cells aged at 70° C. for 0-8 weeks.

FIG. 64A provides a 2D projected curve on the (ΔS, ΔH) plan at 3.94V OCPof LIB cells aged at 60° C. for 0-8 weeks. FIG. 64B provides a 2Dprojected curve on the (ΔS, ΔH) plan at 3.94V OCP of LIB cells aged at70° C. for 0-8 weeks.

FIG. 65 provides a discharge profiles for a LiB cell after everycompleted 100 cycles.

FIG. 66 provides OCP profiles of LIB cells vs. SOC. Cells were subjectedto 1 to 1000 cycles.

FIG. 67 provides entropy profiles of LIB cycled 1 to 1000 cycles vs.SOC.

FIG. 68 provides enthalpy profiles of LIB cycled 1 to 1000 cycles vs.SOC.

FIG. 69 provides entropy profiles of LIB cycled 1 to 1000 cycles vs.OCP.

FIG. 70 provides enthalpy profiles of LIB cycled 1 to 1000 cycles vs.OCP.

FIG. 71 provides a 3D (ΔS, ΔH, N) plot at 3.87V OCP of LIB cells cycled1 to 1000 cycles.

FIG. 72 provides 2D projected curve on the (ΔS, ΔH) plan at 3.87 V OCPof LIB cells cycled 1 to 1000 cycles.

FIG. 73 provides a 3D (ΔS, ΔH, N) plot at 3.94V OCP of LIB cells cycled1 to 1000 cycles.

FIG. 74 provides a 2D projected curve on the (ΔS, ΔH) plan at 3.94V OCPof LIB cells cycled 1 to 1000 cycles.

FIG. 75 provides a 2D projected curve on the (ΔS, ΔH) plan at 3.94V OCPof LIB cells having incurred a capacity loss of 5%.

FIG. 76 provides a 2D projected curve on the (ΔS, ΔH) plan at 3.94V OCPof LIB cells having incurred a capacity loss of 10%.

FIG. 77 provides a 2D projected curve on the (ΔS, ΔH) plan at 3.94V OCPof LIB cells having incurred a capacity loss of 15%.

FIG. 78 provides a 2D projected curve on the (ΔS, ΔH) plan at 3.94V OCPof LIB cells having incurred a capacity loss of 20%.

FIG. 79 provides a 2D projected curve on the (ΔS, ΔH) plan at 3.94V OCPof LIB cells having incurred a capacity loss of 25%.

FIG. 80 provides a 3D profile of LIB before ageing.

FIG. 81 provides OCV Profiles at various aging points (in weeks) at 60°C.

FIG. 82 provides a 3D profile of a 2 week aged cell at 60° C.

FIG. 83 provides a 3D profile of an 8 week aged cell at 60° C.

FIG. 84 provides projected curves (w/SOC).

FIG. 85 provides OCV Profiles at various aging points (in weeks) at 70°C.

FIG. 86 provides 3D profile of 2 week aged cell at 70° C.

FIG. 87 provides 3D profile of 8 week aged cell at 70° C.

FIG. 88 provides projected curves w/SOC.

FIG. 89 provides a 3D profile of charged cell to 4.2V.

FIG. 90 provides a 3D profile of overcharged cell to 4.6V.

FIG. 91 provides a 3D profile of overcharged cell to 4.9V.

FIG. 92 provides projected curves w/SOC.

FIG. 93 provides Entropy and Enthalpy vs. normalized SOC of LIBs uponcycling.

FIG. 94 provides Entropy and Enthalpy vs. OCV of LIBs upon cycling.

FIG. 95 provides ΔS and ΔH vs. OCV of a Graphite Anode.

FIG. 96 provides IC set-up with a chip.

FIG. 97 provides results of a typical temperature and voltage vs. timeprofile for a KL 25 z chip measurement on an Energizer battery.

FIG. 98 provides entropy vs OCV of an Energizer at 610 mAH with Entropydata in blue from BA 2000 and in red from the chip.

FIG. 99. FIG. 98 provides entropy vs OCV of an Energizer at 610 mAH withEntropy data in blue from BA 2000 and in red from the chip.

FIG. 100 provides an SoC assessment from the chip.

FIG. 101 provides Entropy measured by the BA2000: Entropy vs. SoC.

FIG. 102 provides Entropy measured by the BA2000: Entropy vs. SoC(summary).

FIG. 103 provides Enthalpy measured by the BA2000: Enthalpy vs. SoC.

FIG. 104 provides Enthalpy measured by the BA2000: Enthalpy vs. SoC.

FIG. 105 provides Entropy measured by the BA2000: Entropy vs OCV.

FIG. 106 provides Entropy measured by the BA2000: Entropy vs. OCV.

FIG. 107 provides Enthalpy measured by the BA2000: Enthalpy vs. OCV.

FIG. 108 provides Enthalpy measured by the BA2000: Enthalpy vs. OCV.

FIG. 109 provides enthalpy and entropy data corresponding to both OCVand state of charge for an LG 3200.

FIG. 110 provides enthalpy and entropy data corresponding to both OCVand state of charge for an LG 3200.

FIG. 111 provides enthalpy vs. entropy for an LG 3200.

FIG. 112 provides a multidimensional state of charge model for an LG3200 comprising state of charge, change in enthalpy and change inentropy.

FIG. 113 provides enthalpy and entropy data corresponding to both OCVand state of charge for an LG 3000.

FIG. 114 provides enthalpy and entropy data corresponding to both OCVand state of charge for an LG 3000.

FIG. 115 provides enthalpy vs. entropy for an LG 3000.

FIG. 116 provides a multidimensional state of charge model for an LG3000 comprising state of charge, change in enthalpy and change inentropy.

FIG. 117 provides enthalpy and entropy data corresponding to both OCVand state of charge for a SONY 2600.

FIG. 118 provides enthalpy and entropy data corresponding to both OCVand state of charge for a SONY 2600.

FIG. 119 provides enthalpy vs. entropy for a SONY 2600.

FIG. 120 provides a multidimensional state of charge model for a SONY2600 comprising state of charge, change in enthalpy and change inentropy.

FIG. 121 provides enthalpy and entropy data corresponding to both OCVand state of charge for an SS 2500.

FIG. 122 provides enthalpy and entropy data corresponding to both OCVand state of charge for an SS 2500.

FIG. 123 provides enthalpy vs. entropy for an SS 2500.

FIG. 124 provides a multidimensional state of charge model for an SS2500 comprising state of charge, change in enthalpy and change inentropy.

FIG. 125 provides enthalpy and entropy data corresponding to both OCVand state of charge for a PAN 3400.

FIG. 126 provides enthalpy and entropy data corresponding to both OCVand state of charge for a PAN 3400.

FIG. 127 provides enthalpy vs. entropy for a PAN 3400.

FIG. 128 provides a multidimensional state of charge model for a PAN3400 comprising state of charge, change in enthalpy and change inentropy.

FIG. 129 provides enthalpy and entropy data corresponding to both OCVand state of charge comparing SONY 2600, LG 3200 and LG 3000.

FIG. 130 provides enthalpy vs. entropy data comparing SONY 2600, LG 3200and LG 3000.

FIG. 131 shows fixed relaxation voltage at 10% state of charge for threemodels provided in Example 4.

FIG. 132 shows fixed relaxation voltage at 10% state of charge withtemperature represented.

FIG. 133 describes the error in the models at various states of charge.

FIG. 134 describes the entropy computed from BA 2000 compared with theentropy computed from the three models.

DETAILED DESCRIPTION

In general the terms and phrases used herein have their art-recognizedmeaning, which can be found by reference to standard texts, journalreferences and contexts known to those skilled in the art. The followingdefinitions are provided to clarify their specific use in the context ofthe invention.

The term “electrochemical cell” refers to devices and/or devicecomponents that convert chemical energy into electrical energy orelectrical energy into chemical energy. Electrochemical cells typicallyhave two or more electrodes (e.g., cathode and anode) wherein electrodereactions occurring at the electrode surfaces result in charge transferprocesses. Electrochemical cells include, but are not limited to,primary batteries, secondary batteries, galvanic cells, fuel cells andphotovoltaic cells.

The term “multidimensional state of charge profile” refers to arelationship between state of charge and at least two differentthermodynamic parameters, such as a change in enthalpy, a change inentropy or a change in Gibbs free energy. In some embodiments, amultidimensional state of charge profile is empirically determined, forexample, by characterizing the state of charge of an electrochemicalcell as a function of at least two different thermodynamic parameters,such as by characterizing a measured state of charge as a function ofmeasured thermodynamic parameters, including a change in enthalpy, achange in entropy or a change in Gibbs free energy for anelectrochemical cell. In an embodiment, the multidimensional state ofcharge profile is defined by a multidimensional plot, such as a threedimensional plot of state of charge as a function of thermodynamicparameters for an electrochemical cell. For example, in someembodiments, the multidimensional state of charge profile comprises plotof state of charge data as a function of change in enthalpy (ΔH) andchange in entropy (ES). In some embodiments, the multidimensional stateof charge profile is empirically generated by characterization of aspecific electrochemical cell such as thermodynamic characterization.Alternatively, the invention includes methods and systems wherein amultidimensional state of charge profile is empirically generated bycharacterization of a class of electrochemical cells, such aselectrochemical cells having the same cathode, anode and electrolyte ofsame composition. In some embodiments, a multidimensional state ofcharge profile is created and/or stored electronically, for example,within a processor, via software or a combination thereof. Optionallyfor some embodiments, a multidimensional state of charge is a functionof additional parameters, such as parameters corresponding to ambientconditions (e.g., temperature, etc.) or conditions characterizing aspecific application or use of an electrochemical cell (e.g. dischargerate, etc.).

The term “state of health (SOH)” refers to the amount of energy andpower deliverable in a system compared to the best, ideal, rated ortheoretical amount of energy or power when the system is newlyfabricated and tested, such as at 100% state of charge. In embodiments,battery state of health decays or reduces due to electrode andelectrolyte materials degradation, from increases in internal resistanceand from mechanical or chemical effects, such as hardware deformationdue to heat, gazing and corrosion. In embodiments, a metric for state ofhealth assessment is the relative peak power reduction at a specified ordefined state of charge, such as expressed by SOH=100 (P(SOC)/P₀(SOC)),where, SOH refers to the state of health of the electrochemical cell,P(SOC) is the peak power at a state of charge (SOC) of an aged cell andP₀(SOC) is the peak power at a state of charge of a freshly manufacturedand tested cell at the same state of charge (SOC); optionally a state ofcharge of 50% is used in determination of SOH, though other states ofcharge are optionally used as well.

The term “state of safety (SOS)” refers to the likelihood or probabilityof the electrochemical cell to undergo a thermal runaway or otherpotentially unsafe condition. In embodiments, a useful metric for thedetermination of state of safety is the onset temperature of a thermalevent within the electrochemical cell at a defined state of charge. Inembodiments, the lower the onset temperature, such as that measured by athermal analysis method including calorimetric methods, differentialthermal analysis (DTA) methods and differential scanning calorimetricmethods (DSC), the higher the thermal runaway risk and thus the lowerthe SOS.

The term “open circuit voltage” refers to the difference in potentialbetween terminals (i.e. electrodes) of an electrochemical cell when thecircuit is open (i.e. no load conditions). Under certain conditions theopen circuit voltage can be used to estimate the composition of anelectrochemical cell. The present methods and system utilizemeasurements of open circuit voltage for thermochemically stabilizedconditions of an electrochemical cell to determine thermodynamicparameters, materials properties and electrochemical properties ofelectrodes, electrochemical cells and electrochemical systems.

The term “capacity” is a characteristic of an electrochemical cell thatrefers to the total amount of electrical charge an electrochemical cell,such as a battery, is able to hold. Capacity is typically expressed inunits of ampere-hours.

The expression “state of charge” or “SOC” is a characteristic of anelectrochemical cell or component thereof (e.g. electrode—cathode and/oranode) referring to its available capacity, such as a battery, expressedas a percentage of its rated or theoretical capacity. The expression“state of charge” can optionally refer to a true state of charge or acoulometric state of charge. The state of charge of an electrochemicalcell can be measured using a variety of methods, including thosedescribed herein. The following references, hereby incorporated byreference, disclose methods for estimating, calculating or measuring astate of charge of an electrochemical cell: Ng et al., Applied Energy 86(2009) 1506-1511; Piller et al., J. Power Sources 96 (2001) 113-120;Coleman et al., IEEE Trans. Ind. Electron. 54 (2007) 2250-2257; Ng etal., “An enhanced coulomb counting method for estimating state-of-chargeand state-of-health of lead-acid batteries,” INTELEC 31st, Incheon, K R,2009; Snihir et al., J. Power Sources 159:2 (2006) 1484-1487;

The term “host material” refers to a component of an electrochemicalcell configured for accommodating a molecule, atom, ion and/or groupinto the host material. In this context, accommodating includesinsertion of a molecule, atom, ion and/or group into the host material,intercalation of a molecule, atom, ion and/or group into the hostmaterial and/or reaction of a molecule, atom, ion and/or group with thehost material. In embodiments, accommodation of a molecule, atom, ionand/or group is a reversible process, such that a molecule, atom, ionand/or group can be released from the accommodating host material. Forcertain embodiments, reversible accommodation by host materials does notresult in significant degradation or significant structural deformationof the material upon multiple accommodation/release cycles. In someembodiments a host material is an intercalation material. In someembodiments a host material is a framework material. In some embodimentsa host material is a host electrode of an electrochemical cell and/or anintercalation electrode of an electrochemical cell.

“Intercalation” refers to refers to the process wherein an ion insertsinto a host material to generate an intercalation compound via ahost/guest solid state redox reaction involving electrochemical chargetransfer processes coupled with insertion of mobile guest ions, such asfluoride ions. Major structural features of the host material arepreserved after insertion of the guest ions via intercalation. In somehost materials, intercalation refers to a process wherein guest ions aretaken up with interlayer gaps (e.g., galleries) of a layered hostmaterial. Examples of intercalation compounds include, but are notlimited to, fluoride ion intercalation compounds wherein fluoride ionsare inserted into a host material, such as a layered fluoride hostmaterial or carbon host material.

“Embed” or “imbed” interchangeably refer to the arrangement of a firstdevice or device component with relation to a second device or devicecomponent such that the two devices or device components are includedwithin a common housing. In one embodiment, a device is embedded withina second device when they are packaged together. In a certainembodiment, a device is embedded within a second device when the devicesare inextricably inseparable, or only separable by destroying ordisassembling one of the devices.

“Thermal communication” refers to the arrangement of two or more devicesor device components such that heat energy can efficiently flow betweenthe devices or device components, either directly or indirectly by meansof an intervening component or material. In some embodiments, twodevices positioned in thermal communication are positioned in physicalcontact. In some embodiments, two devices positioned in thermalcommunication have an intermediate material positioned between them,such as a material that is an efficient conductor of heat, such ascomprising aluminum or copper. In one embodiment, two devices or devicecomponents that are positioned in thermal communication have the sametemperature.

“Electrical communication” refers to the arrangement of two or moredevices or device components such that electrons can efficiently flowbetween the devices or device components. In an embodiment, two devicespositioned in electrical communication are positioned in physicalcontact. In an embodiment, two devices positioned in electricalcommunication are positioned such that an electrical conductor ispositioned between them, such as a copper wire or other metallic wire orconductor. “Switchable electrical communication” refers to thearrangement of two or more devices or device components such that theflow of electrons between two or more devices can be selectivelyterminated, for example using a switch. In one embodiment, three or moredevices are in switchable electrical communication when, at any onetime, only two of the three or more devices are in electricalcommunication with one another. In one embodiment, three or more devicesare in switchable electrical communication when one device may beselectively placed into electrical communication with any one or more ofthe other two or more devices. In one embodiment, two or more devicesare in switchable electrical communication when one device may beselectively placed into electrical communication with any one or more ofthe other devices.

“Data communication” refers to the arrangement of two or more devices ordevice components such that data can be transmitted between the devicesor device component. Data communication includes one way and two waydata transport. Data communication may be wired or wireless. In anembodiment, two devices or device components in data communication arein electrical communication. “Switchable data communication” refers tothe arrangement of two or more devices or device components such thatthe transmission of data between two or more devices can be selectivelyterminated. In one embodiment, three or more devices are in switchabledata communication when, at any one time, only two of the three or moredevices are in data communication with one another. In one embodiment,two or more devices are in switchable data communication when one devicemay be selectively placed into data communication with any one or moreof the other devices.

“Temperature sensor” refers to a device used to provide a signalindicative of a temperature of an object. In embodiments, a temperaturesensor provides a voltage or a resistance to indicate the temperature ofan object.

“Current monitoring circuit” refers to a circuit which receives acurrent and provides an indication of a magnitude or direction ofcurrent flow through the current monitoring circuit. In embodiments, anindication provided by a current monitoring circuit is a dataindication, a visual indication or an electrical indication, such as avoltage indication or a current indication. In embodiments, a currentmonitoring circuit monitors a current from an electrochemical cell, forexample a charging current or a discharging current. In embodiments, acurrent monitoring circuit continuously or periodically monitors acurrent.

“Circuit for determining an open circuit state” refer to a circuit whichmonitors whether or not an electrochemical cell is operating under opencircuit voltage conditions. In embodiments, a circuit for determining anopen circuit state comprises a current monitoring circuit. Inembodiments, a circuit for determining an open circuit state comprises apower switching circuit.

“Open circuit state” refers to a configuration of an electrochemicalcell providing a measure of whether the electrochemical cell isoperating under open circuit voltage conditions. In embodiments, anelectrochemical cell is operating under open circuit voltage conditionswhen a current flowing into or from the electrochemical cell is zero oris below a specified threshold value.

“Temperature monitoring circuit” refers to a circuit which receives asignal indicative of an object's temperature and calculates, derives,computes or otherwise determines or measures the object's temperature.In embodiments, a temperature monitoring circuit continuously monitorsan object's temperature. In embodiments, a temperature monitoringcircuit periodically monitors an object's temperature.

“Voltage monitoring circuit” refers to a circuit which receives a signalvoltage from another object or device. In embodiments, a voltagemonitoring circuit continuously monitors a voltage. In embodiments, avoltage monitoring circuit periodically monitors a voltage.

A “circuit for determining a thermodynamic parameter” refers to acircuit which computes, derives, calculates or otherwise determines ormeasures a thermodynamic state function or a change in a thermodynamicstate function, including, but not limited to, the thermodynamic statefunctions of Enthalpy (H), Entropy (S) and Gibbs Free Energy (G). Inembodiments, a circuit for determining a thermodynamic parameterdetermines a change in a thermodynamic state function from measurementsof an electrochemical cell's open circuit voltage, temperature,composition and/or state of charge.

A “temperature controller” and a “means for controlling or establishinga temperature” refer to a device having the ability to activelyestablish and control its own temperature or a temperature of a deviceit is in thermal communication with or a device used for controlling theaddition or heat to an external component.

A “field programmable gate array” or “FPGA” refers to a circuit orcircuit component which can have its functionality defined afterconstruction or fabrication. In an embodiment, an FPGA is a component ofan integrated circuit. In embodiments, some integrated circuits comprisean FPGA. FPGAs are useful, for example, for providing desiredfunctionality to an integrated circuit, such as to enable digital and/oranalog signal processing.

An “application specific integrated circuit” or “ΔSIC” refers to acircuit or circuit component which has its functionality defined duringconstruction or fabrication.

A “current monitoring circuit” refers to a circuit which measures ormonitors a current being delivered by or delivered to another object ordevice, such as an electrochemical cell. In embodiments, a currentmonitoring circuit continuously monitors a current. In embodiments, acurrent monitoring circuit periodically monitors a current. Inembodiments, a current monitoring circuit calculates a total amount ofcurrent delivered to or from another object or device, such as anelectrochemical cell. In embodiments, a current monitoring circuitcomprises a coulometer, a galvanometer or an ammeter.

The terms “true state of charge” and “thermodynamic state of charge”interchangeably refer to a fractional or percentage of the actual chargecapacity remaining in an electrochemical cell as compared to theoriginal, theoretical, or maximum capacity of charge in theelectrochemical cell. In embodiments, the true state of charge of anelectrochemical cell is determined by comparing a condition of theelectrochemical cell, such as one or more thermodynamic parameters, witha condition of a reference electrochemical cell and identifying the truestate of charge of the electrochemical cell as the state of charge ofthe reference electrochemical cell having the same condition as theelectrochemical cell.

The term “Coulometric state of charge” refers to a fractional orpercentage of the charge capacity remaining in an electrochemical cellas compared to the original, theoretical, or maximum capacity of chargein the electrochemical cell and measured by integrating a currentactually delivered by or to the electrochemical cell. In embodiments,the Coulometric state of charge and the true state of charge can bedifferent, such as when side reactions take place in an electrochemicalcell that do not contribute to charging or discharging the electrodes ofthe electrochemical cell but are still associated with delivery ofcurrent from or to the electrochemical cell. Such side reactionsinclude, but are not limited to, oxidation of an electrolyte in theelectrochemical cell and reduction of electrochemical cell. Inembodiments a Coulometric state of charge is determined by subtractingthe total measured charge delivered by the electrochemical cell(including any charging and discharging of the electrochemical cell)from the original, theoretical or maximum charge capacity of theelectrochemical cell and dividing by the original, theoretical ormaximum charge capacity of the electrochemical cell.

The term “thermochemically stable” refers to a state in which theelectrochemical cell is substantially at equilibrium with regards totemperature and chemical activity. In an embodiment, thermochemicallystable refers to a state in which changes in enthalpy and entropy may beeffectively measured.

The present invention provides methods and systems for thermodynamicallyevaluating electrochemical systems and components thereof, includingelectrochemical cells such as batteries, fuel cells and photovoltaics.The present systems and methods are capable of monitoring selectedelectrochemical cell conditions, such as temperature and composition,and carrying out measurements of a number of cell parameters, includingopen circuit voltage, time and temperature, with accuracies large enoughto allow for precise determination of thermodynamic state functions andmaterials properties relating to the composition, phase andelectrochemical properties of electrodes and electrolytes in anelectrochemical cell. Thermodynamic measurement systems of the presentinvention are highly versatile and provide information for predicting awide range of performance attributes for virtually any electrochemicalsystem having an electrode pair.

FIG. 1 illustrates an exemplary embodiment of a device of the presentinvention constructed as an integrated circuit 100. Integrated circuit100 comprises multiple internal circuit components including an AC to DCconverter 101 for converting from mains electricity 102 (e.g., AC100-240 V) to DC voltages useful for providing power to other circuitcomponents. AC to DC converter 101 is optionally provided as a separatecomponent from integrated circuit 100, for example to reduce thecomplexity and size of integrated circuit 100, in which case DC voltagesare directly provided to other circuit components of integrated circuit100. The DC voltage output of AC to DC converter 101 is optionallyadjustable to provide various DC voltages depending on the powerrequirements of other circuit components of integrated circuit 100.Optional input/output circuit 103 provides for data communication withan input/output device 104 (e.g., as a keyboard, touch screen ordisplay), to obtain input from and display information to a user.Input/output circuit 103 receives information from display circuit 105for displaying to a user on input/output device 104, such as computationresults received from sub-circuit 106. Input/output circuit 103 providesinformation to command circuit 107 for converting user input frominput/output device 104 to commands for sub-circuit 106. Sub-circuit 106provides various functionality to integrated circuit 100, includingvoltage, current and temperature monitoring, voltage, current andtemperature control, and a processor for determining thermodynamicparameters and conditions of an electrochemical cell 108 under test. Inthis embodiment, a temperature control circuit 109 provides controlsignals to temperature controller 110, which is positioned in thermalcommunication with electrochemical cell 108. Temperature controller 110optionally comprises a thermoelectric cooler (TEC) and heat sink. Thetemperature 111 of temperature controller 110 and/or electrochemicalcell 108 is provided to microcontroller 112, which comprises atemperature monitoring circuit. The voltage or current 113 ofelectrochemical cell 108 is also monitored by microcontroller 112, whichcomprises a voltage monitoring circuit, for example for monitoring anopen circuit voltage of electrochemical cell 108. Microcontroller 112optionally comprises a field programmable gate array circuit or anothercircuit having the desired functionality for measuring temperature,voltage and computing thermodynamic parameters and electrochemical cellconditions. In this embodiment, a voltage and current control circuit114 provides voltage and/or current 115 to electrochemical cell 108, forexample for charging electrochemical cell 108. Optionally, voltage andcurrent control circuit 114 also provides voltage and current monitoringof electrochemical cell 108, thereby relieving microcontroller 112 fromhaving to monitor voltage or current 113 of electrochemical cell 108.FIG. 3 illustrates a block diagram for a electrochemical thermodynamicmeasurement system including temperature control components.

In embodiments, inclusion of temperature control circuitry andtemperature control hardware adds complexity, size and cost to a deviceof the present invention. Instead, natural temperature changes of anelectrochemical cell as it is charged and discharged can be exploited toobtain measurements on an electrochemical cell at various temperatures.FIG. 2 illustrates an exemplary embodiment of a device of the presentinvention that does not include a temperature controller or associatecontrol circuitry. In this embodiment, integrated circuit 200 comprisesmultiple internal circuit components including an AC to DC converter 201for converting from mains electricity 202 (e.g., AC 100-240 V) to DCvoltages useful for providing power to other circuit components. AC toDC converter 201 is optionally provided as a separate component fromintegrated circuit 200, for example to reduce the complexity, size andcost of integrated circuit 200, in which case DC voltages are directlyprovided to other circuit components of integrated circuit 200. The DCvoltage output of AC to DC converter 201 is optionally adjustable toprovide various DC voltages depending on the power requirements of othercircuit components of integrated circuit 200. Optional input/outputcircuit 203 provides for data communication with an input/output device204 (e.g., as a keyboard, touch screen or display), to obtain input fromand display information to a user. Input/output circuit 203 receivesinformation from display circuit 205 for displaying to a user oninput/output device 204, such as computation results received fromsub-circuit 206. Input/output circuit 203 provides information tocommand circuit 207 for converting user input from input/output device204 to commands for sub-circuit 206. Sub-circuit 206 provides variousfunctionality to integrated circuit 200, including temperature, voltageand current monitoring and voltage and current control, and a processorfor determining thermodynamic parameters and conditions of anelectrochemical cell 208 under test. The temperature 211 ofelectrochemical cell 208 is provided to microcontroller 212, whichcomprises a temperature monitoring circuit. The voltage or current 213of electrochemical cell 208 is also monitored by microcontroller 212,which comprises a voltage monitoring circuit, for example for monitoringan open circuit voltage of electrochemical cell 208. Microcontroller 212optionally comprises a field programmable gate array circuit or anothercircuit having the desired functionality for measuring temperature,voltage and computing thermodynamic parameters and electrochemical cellconditions. In this embodiment, a voltage and current control circuit214 provides voltage and/or current 215 to electrochemical cell 208, forexample for charging electrochemical cell 208. Optionally, voltage andcurrent control circuit 214 also provides voltage and current monitoringof electrochemical cell 208, thereby relieving microcontroller 212 fromhaving to monitor voltage or current 213 of electrochemical cell 208.

FIG. 4 illustrates an embodiment of a device of the present inventioncomprising a circuit for determining a thermodynamic parameter. Forexample, the embodiment shown in FIG. 4 comprises an entropy monitoringcircuit 400. A temperature sensor 401 is positioned in thermalcommunication to the cathode or anode of the electrochemical cell 402.Useful temperature sensors 401 include, but are not limited tothermocouple, thermistor, diode or transistor based temperature sensors.As used herein the term thermistor refers to a resistive element wherethe resistance value changes according to the temperature, therebypermitting determination of temperature by measuring the resistance ofthe thermistor. A current sensor 403 is positioned in electricalcommunication with the electrochemical cell, and is useful fordetermining if the electrochemical cell 402 is under open circuitvoltage conditions, for example, when no current is flowing into or fromthe electrochemical cell, thereby permitting a determination of the opencircuit voltage of the electrochemical cell 402. The entropy monitoringcircuit 400 shown in FIG. 4 comprises a power conditioning circuit 404,a temperature-voltage converter 405, voltage differentiators 406 and407, a division circuit 408 and a modulation circuit 409. One or moreinductors 410 are positioned in electrical communication with theelectrochemical cell. In embodiments, the output of modulation circuit409 is either a frequency modulated or phase shift modulated voltagesignal that contains information related to the change in voltage of theelectrochemical cell as a function of time (dV/dt). The inductors 410are useful for blocking an AC signal from reaching the electrochemicalcell 402 and any load 411. The power conditioning circuit 404 providespower to the monitoring circuit 400 and can cut off the power to themonitoring circuit 400 when the electrochemical cell 402 is not in useto prevent unnecessarily draining the energy stored in theelectrochemical cell 402.

Power conditioning circuit 404 also operates to provide power to themonitoring circuit 400 only when the electrochemical cell 402 is underopen circuit conditions such that monitoring circuit 400 does notconsume additional energy unnecessarily. Power conditioning circuit 404also serves to convert voltage from electrochemical cell 402 to voltagesrequired for operation of various components of monitoring circuit 400.FIG. 5 illustrates an exemplary power switching circuit embodiment.Here, the output 501A of flip-flop 502 changes from low logic to highlogic when the input signal 503 changes from high logic to low logic.The input signal 503 corresponds to a current measurement signal of theelectrochemical cell 504. A change from high logic to low logic in inputsignal 503 corresponds to stopping the current being supplied byelectrochemical cell 504, such as occurs when under open circuit voltageconditions, indicating that the open circuit voltage can be captured.When the output logic 501A is high, transistor 505 is turned on,allowing the monitoring circuit to be turned on by connecting the anodefrom electrochemical cell 504 to a switching mode power supply 506 whichpowers the monitoring circuit. An RC circuit 507, such as having aresistor and capacitor in parallel, is provided at the reset pin 508 offlip-flop 502 for turning off the monitoring circuit, such as after apre-set time or if the electrochemical cell 504 is permanently shut offor put into open circuit voltage mode. This is useful for powering offswitching mode power supply 506 and preventing the monitoring circuitfrom continuing to drain electrochemical cell 504. When electrochemicalcell 504 is providing current, flip-flop output 501B is high logic, andtherefore, transistor 509 is turned on and the capacitor in RC circuit507 is charging. When the electrochemical cell 504 is open circuit,flip-flop output 501B is low logic and the capacitor in RC circuit 507will be discharged through the resistor in RC circuit 507. After sometime, the capacitor will become discharged and the voltage at reset pin508 will become zero and this will reset flip-flop 502 such that flipflop output 501A becomes low logic and cuts off power supply 506 fromdelivering power to the monitoring circuit.

The voltage provided by the electrochemical cell 505 is optionallyconverted to different supply voltages for different sub-circuits, andthis can be achieve using a switching mode power supply, such ascomprising a voltage converting circuit. FIGS. 6A and 6B illustrate twoexemplary voltage converting circuit embodiments. FIG. 6A illustrates aboost converter circuit embodiment that increases a voltage, forexample, converting 3.0 V to 9 V and 15 V. FIG. 6B illustrates a Buckconverter circuit embodiment that reduces a voltage, for example,converting 3.0 V to 1.5 V.

Temperature-voltage converter 405 is used to convert the temperature ofelectrochemical cell 402 sensed by temperature sensor 401 into voltage.In embodiments, the conversion is such that the converted voltage islinearly proportional to the temperature of electrochemical cell 402.FIG. 7 illustrates an exemplary temperature-voltage converterembodiment. In the embodiment shown in FIG. 7, the temperature ismeasured as a resistance, such as a change in resistance value (R_(T))due to temperature. In the circuit embodiment shown in FIG. 7, three offour resistors have a resistance R, while the fourth has a resistanceR+R_(T). Here, V1=V·R/(R+R)=V/2 and V−V2/R=(V2−V_(out))/(R+R_(T)) andV_(out)=−V·R_(T)/2·R and thus V_(out) is linearly proportional to theresistance change due to temperature R_(T).

Voltage differentiators 406 and 407 perform time differentiation of avoltage. In this embodiment, voltage differentiators 406 and 407respectively provide dV/dt and dT/dt, where V is the open circuitvoltage and T is the temperature (expressed in voltage) ofelectrochemical cell 402 and t is time. FIG. 8 illustrates an exemplaryvoltage differentiator embodiment.

Division circuit 408 is used to perform division of two circuits. Inthis embodiment, the signals are dV/dt and dT/dt, which provides dV/dTby the division. FIG. 9 illustrates an exemplary division circuitembodiment.

As no additional electrodes are to be introduced into electrochemicalcell 402, the signal that contains dV/dt will be accessed through thetwo existing electrodes of electrochemical cell 402. Hence, the signalwill be modulated by modulation circuit 409, for example, using eitherfrequency or phase shift modulation for a specific carrier frequencysuch that the signal can be later extracted through an electronic filterwithout the influence of other noise. In addition, such a time varyingsignal will also not impact the load current and electrochemical cell402 by using inductors 410 described above. FIGS. 10A and 10B illustrateexemplary modulation circuit embodiments. FIG. 10A depicts a typicalhigh frequency sine wave generator for the carrier; FIG. 10B illustratesa typical frequency modulation circuit, where the input from thedivision circuit is provided at the Mic/ECM location and the antenna(denoted as A) is the output, optionally transmitted wirelessly orconnected to the electrochemical cell, such as at the anode.

To further demonstrate the components, performance and functionality ofthe present systems and methods, entropies and enthalpies ofelectrochemical reactions taking place at an anode or a cathode isexamined. First, a general background explanation is provided,establishing the relationships between experimental measurementsprovided and important thermodynamic parameters which govern importantelectrochemical properties of the electrode. Second, a description ofthe components of the measurement system is provided.

To determine the evolution of the entropy and enthalpy of a reactiontaking place at an electrode, such as lithium intercalation into amaterial Li_(x)M as a function of x, the temperature dependence of theopen circuit voltage is examined using the present invention. Thisvoltage is related to the Gibbs free energy of reaction by thethermodynamic identity:

ΔG=−nFU

where U is the equilibrium potential of the electrode and F the Faradaynumber. For the Li⁺/Li electrochemical couple one electron is exchanged,so n=1.

The partial molar enthalpy, ΔH, and entropy, ΔS, of the reaction arederived with respect to the amount of charge passed. In the following,ΔH and ΔS are assumed independent of temperature. Although manymeasurements are made at varying temperatures, this assumption may bereliable as long as there are no phase transitions in the measuredtemperature range. Such is, for instance, the case for lithium cobaltoxide at the composition Li_(0.5)CoO₂, where a slight temperature changetriggers the monoclinic to hexagonal phase transition close to roomtemperature.

The values measured are partial molar variables. From the first law ofthermodynamics relating the internal energy of the system E to the workWand heat dissipated Q, the differential of the enthalpy can beobtained:

$\begin{matrix}{{d\; E} = {{\delta \; W} + {\delta \; Q}}} \\{= {{{- P}\; d\; V} + {\mu \; d\; n} + {T\; d\; S}}}\end{matrix}$ $\begin{matrix}{{d\; H} = {{d\; E} + {P\; d\; V} + {V\; d\; P}}} \\{= {{\mu \; d\; n} + {T\; d\; S} + {V\; d\; P}}}\end{matrix}$

with μ, the chemical potential of the cathode, referred to the metalliclithium anode, and n is the number of lithium atoms exchanged. The termμdn is the electrical work of the charge exchanged. In this study, thepressure P is constant, so the third term, VdP, is neglected. Using (6)the Gibbs free energy can then be written as:

$\begin{matrix}{{d\; G} = {{d\; H} - {T\; d\; S} - {S\; d\; T}}} \\{= {{\mu \; d\; n} - {S\; d\; T}}}\end{matrix}$

To get molar values we use x=n/N, where N is Avogadro's number. Thechemical potential is related to the open circuit voltage U by μ=−eUwhere e is the charge of the electron.

$\begin{matrix}{{d\; G} = {{{- N}\; e\; U\; d\; x} - {S\; d\; T}}} \\{= {{{- {FU}}\; d\; x} - {S\; d\; T}}}\end{matrix}$

Since F=Ne. Then using Maxwell's relation for mixed second derivatives,we get the partial molar entropy of lithium intercalation as a functionof the open circuit voltage:

${\frac{\partial S}{\partial x}_{T}} = {{{F\frac{\partial U}{\partial T}}_{x}} = {\Delta \; S}}$

Since by definition H=G+TS we find:

$\begin{matrix}{{\frac{\partial H}{\partial x}_{T}} = {\frac{\partial G}{\partial x}_{T}{{{+ T}\frac{\partial S}{\partial x}}_{T}}}} \\{= {{N\frac{\partial G}{\partial n}}_{T}{{{+ {TF}}\frac{\partial U}{\partial T}}_{x}}}}\end{matrix}$

By definition (∂G/∂n)_(T) is the chemical potential μ=−eU. We thusobtain the partial molar enthalpy of lithium intercalation as a functionof the open circuit voltage, U:

${\frac{\partial H}{\partial x}_{T}} = {{{{{- F}\; U} + {{TF}\frac{\partial U}{\partial T}}}_{x}} = {\Delta \; H}}$

It must be noted that μ=μ_(c)−μ_(a), is the difference of chemicalpotential between the cathode and the anode. As a consequence all ourresults are referred to the lithium anode, for which the chemicalpotential is supposed to be a constant at different states of charge.

The invention may be further understood by the following non-limitingexamples.

Example 1 The Imbedded Chip

The devices described in this example are designed to be imbedded in anelectrochemical cell. Optionally, the chip can be imbedded in a batterymodule, such as a module comprising 2 to 20 electrochemical cells, andin a battery pack, such as comprising 1 to 100 modules). The imbeddedchip is designed to collect current, voltage and temperature data withinindividual cells and convert them to useful thermodynamics data in orderto assess the battery state of health and state of charge.

The block diagram shown in FIG. 3 illustrate the configuration of anelectrochemical thermodynamics measurement system (ETMS). The ETMScomprises a thermoelectric couple (TEC) module for controlling thetemperature of one or more electrochemical cells, as well as temperaturecontrol components, voltage and current monitoring and controlcomponents, power supply components and various data and communicationscomponents. In embodiments, devices of the present inventionspecifically exclude temperature control components, such as thethermoelectric couple module and associate control circuitry. Inembodiments, devices of the present invention utilize temperaturechanges that occur naturally as an electrochemical cell is heated duringcharging or discharging or that occur naturally as an electrochemicalcell relaxes towards ambient temperature after charging or dischargingis halted.

Optionally, a number of functions of the ETMS can be implemented in asingle chip. FIG. 1 illustrates a block diagram showing theconfiguration of the ETMS incorporated into a single chip. Thefunctionality of such a single chip system is optionally different fordifferent applications. For example, for a personal computer or laptopbattery, the cell data is optionally collected automatically by thesingle chip that provides data periodically to the PC, where state ofhealth or other cell conditions calculations are performed by softwarerunning on the PC. In other applications, the calculations of state ofhealth or other cell conditions are optionally made within the singlechip itself.

Example 2 Non-Equilibrium Measurements of Open Circuit Voltage

In embodiments, devices of the present invention are incorporated intoelectrochemical cells and systems drawing power from electrochemicalcells. After charging or discharging of an electrochemical cell ishalted, it may take time for the electrochemical cell to reachequilibrium or thermochemically stabilized conditions. For certainembodiments, the devices may seldom have the opportunity to measure anelectrochemical cell's open circuit voltage when the electrochemicalcell is at equilibrium. For these embodiments, the open circuit voltageneeds to be estimated without having to wait for the electrochemicalcell to reach equilibrium. In embodiments, the change of open circuitvoltage of an electrochemical cell after charging or discharging of theelectrochemical cell is halted follows an exponential decay shape. Bymonitoring a period of the exponential decay of open circuit voltage,the time constant for the exponential decay can be determined and theasymptotic value that the exponential decay is approaching (i.e., theequilibrium value) can be estimated.

Example 3 Comparison Between Controlled and Uncontrolled Temperature

Four 18650 lithium ion cells were subjected to two separate tests. Inthe first, thermodynamics parameters were measured using controlledtemperature. The state of charge of the cells was change by 5%increments and at each state of charge the cell's open circuit voltagewas measured during cooling from 25° C. to 10° C. in a cell holderequipped with temperature control, enabling ΔS and ΔH of the cell to becalculated at each state of charge.

In the second test, the cells were charged to 4.2 V and then dischargedto a pre-defined state of charge: 98% (cell 1), 65% (cell 2), 40% (cell3) and 3% (cell 4). A thermocouple was attached to each cell and thecells were heated in an oven to about 55° C., simulating natural heatingby charging or discharging. The cells were taken out of the oven andcovered with a thermal isolation material. The cells' temperatures andthe open circuit voltages were monitored as the cells cooled to theambient temperature. Using the open circuit voltage versus temperatureprofiles, ΔS and ΔH were calculated for each cell.

FIGS. 11-14 illustrates data obtained for the four cells in which thetemperature of the cells was not controlled. FIG. 15 provides a summaryof the analysis results of FIGS. 11-14. FIG. 16 illustrates data showinga comparison of open circuit voltage data obtained with and withouttemperature control. FIG. 17 illustrates data showing a comparison ofmeasurements of open circuit voltage obtained with and withouttemperature control. FIG. 18 illustrates data showing a comparison ofmeasurements of changes in entropy obtained with and without temperaturecontrol. FIG. 19 illustrates data showing a comparison of measurementsof changes in enthalpy obtained with and without temperature control.

The results of the comparison illustrate that thermodynamics data,including open circuit voltage, ΔS and ΔH, can be obtained at differentstates of charge without temperature control, i.e., during cell coolingto ambient temperature. These data are consistent with that measuredwith active control over cell conditions, including SOC and temperature.This comparison illustrates that temperature control is not essential tomeasure thermodynamics data on an electrochemical cell.

The comparison also provides useful insights to determination of thetrue or thermodynamic state of charge of an electrochemical cell. As theelectrochemical cell is charged and discharged under non-controlledconditions, side reactions can take place, such as oxidizing or reducingthe electrolyte or other reactions that do not contribute to charging ordischarging the cell electrodes. Under conditions where side reactionsare taking place, measurement of the cell's SOC by a Coulometricmeasurement, such as Coulomb counting or current integration, will notprovide a true measurement of the cell's SOC. Because the measuredthermodynamics data under non-controlled temperature conditions areconsistent with those measured under carefully controlled temperatureconditions, the non-controlled temperature data can be used to determinethe true SOC of the electrochemical cell. For example, the true SOC of atest electrochemical cell operating under non-controlled conditions canbe obtained as the SOC for an equivalent chemistry electrochemical cellunder controlled conditions having the same thermodynamics parameters asthose measured for the test electrochemical cell operating undernon-controlled conditions.

Example 4 State of Health and State of Safety Determination

This example describes the principle of assessment methods fordetermination of a state of safety (SOS) and state of health (SOH) of anelectrochemical cell. Differential entropy and differential enthalpy ata defined state of charge (SOC) or open circuit voltage (OCV) can beused to assess an electrochemical cell's SOH and SOS. SOH relates to thecell's energy storage performance decay due to materials degradation ascomponents of the cell age. Capacity loss and discharge voltagedecreases are among the SOH metrics for electrochemical cells.

In the differential thermodynamics measurements technique,thermodynamics data (e.g., ΔS and ΔH) are measured on a cell before andafter aging of the cell. Differential entropy (dS) and differentialenthalpy (dH) are obtained by taking the difference between theentropy/enthalpy data before and after aging at each SOC:dS(SOC)=ΔS(SOC)_(after aging)−ΔS(SOC)_(before aging) anddH(SOC)=ΔH(SOC)_(after aging)−ΔH(SOC)_(before aging).

Three experiments were performed to examine the effects of acceleratedaging on Lithium Ion Battery (LIB) cells, in particular with respect tothe SOH of the cells. In the first experiment, aging of lithium ioncells was investigated due to thermal aging. Here, lithium ion cellswere cycled between 2.75 V and 4.2 V at 10 mA (˜C/4 rate) for fourcycles then cells were charged to 4.2 V and stored in an oven at 60° C.and 70° C. for a period of time up to 8 weeks. At the end of each week,four cells were retrieved and tested by galvanostatic charge anddischarge and thermodynamics measurements were performed.

FIGS. 19 and 20 provide data illustrating the discharge profiles ofcells aged at 60° C. and 70° C., respectively, over a period of 8 weeks.The data show a decrease in the capacity and cell potential as the cellsage over time. FIGS. 21A and 21B provide a summary of the dischargecharacteristics after aging at 60° C. and 70° C., respectively. Here,Q_(d) is discharge capacity, CL is Capacity loss, <E> is Averagedischarge voltage, ε_(d) is discharge energy and is equal to Q_(d)x<E>and SOH is 100-CL.

FIG. 22 provides data illustrating the entropy profiles of LIB cellsaged at 70° C. over a period of 8 weeks. FIG. 23 provides dataillustrating the enthalpy profiles of LIB cells aged at 70° C. FIG. 24provides data illustrating differential entropy profiles of LIB cellsaged at 70° C. FIG. 25 provides data illustrating differential enthalpyprofiles of LIB cells aged at 70° C. As indicated in the figures, a SOCof 5% and 80% are where dS and dH show the most significant changes inintensity. These states of charge correspond to changes in the anode andthe cathode, respectively. Accordingly, 5% and 80% SOC will be used forall other aging methods to assess SOH vs. dS

FIG. 26 illustrates data providing the state of health versusdifferential entropy of cells aged at 60° C., and shows a more rapiddecrease in the state of health of the cathode over time compared to theanode. FIG. 27 illustrates data providing the state of health versusdifferential entropy of cells aged at 70° C., and again shows a morerapid decrease in the state of health of the cathode over time comparedto the anode.

In the second experiment, aging of lithium ion cells was investigateddue to overcharging. Coin cells rated at about 43 mAh were chargedgalvanostatically under a 10 mA rate up to a fixed cut-off voltage (COV)between 4.2 V and 4.9 V. A constant COV plateau was then applied for 1hour. For each set of tests four new cells were used and the COV wasincreased by 0.1 V. Accordingly, different cells were charged to 4.2V,4.3 V, 4.4 V and so on up to 4.9 V. The cells were then discharged to2.75 V and charged to 4.2 V followed by a discharge to 2.75 V under 6mA. The cells were then transferred to an electrochemical thermodynamicmeasurement system (BA-1000) to evaluate the cell's thermodynamicscharacteristics.

FIG. 28 provides data illustrating the discharge profile of cellsovercharged at different cut-off voltages (COV). Here, the cellsgenerally exhibit a decrease in potential and capacity as the cells ageby overcharging. FIG. 29 summarizes the discharge characteristics afterovercharging at different COV. FIG. 30 provides data showing entropyprofiles at different charge cut-off voltages. FIG. 31 provides datashowing enthalpy profiles at different charge cut-off voltages.

FIG. 32 illustrates data providing the state of health versusdifferential entropy of overcharged cells, and shows an initially morerapid decrease in the state of health of the cathode for amount ofovercharge, but as the cells are more and more overcharged the state ofhealth of the anode begins a more rapidly decrease than the cathode.

In the third experiment, aging of lithium ion was investigated due tolong cycle aging. Here, four cells were cycled gavanostatically at 20 mA(˜C/2 rate) between 2.75 V and 4.2 V at ambient temperature. After eachcompleted 100 cycles; the cells were analyzed by galvanostatic cyclingand thermodynamics measurements were performed. The same cells were thencycled again for an additional 100 cycles until reaching 1000 cycles.

FIG. 33 provides a summary of discharge characteristics of the cellsafter cycling. FIG. 34 provides data showing differential entropyprofiles of cells after cycling. FIG. 35 provides data showingdifferential enthalpy profiles of cells after cycling.

FIG. 36 illustrates data providing the state of health versusdifferential entropy of cycled cells, and shows an initially more rapiddecrease in the state of health of the cathode for as the number ofcycles increases, but as the cells are further cycled, the state ofhealth of the anode begins a more rapid decrease than the cathode.

As the above examples illustrate, regardless of the aging method(thermal, overcharge or cycling), dS and dH increase with aging rate.Capacity losses also increase with the aging rate. The cells' SOH, asdetermined from capacity loss using a simple relationship of SOH=100-CL,decrease with both dS and dH.

To investigate the effects of aging on the state of health of anelectrochemical cell, experiments were performed on electrochemicalcells. In particular, three cells were utilized to investigate theeffects of aging on a self-heating rate (SHR) taking place within thecells, including a fresh cell, a cell thermally aged at 70° C. for 1week and a cell thermally aged at 70° C. for 2 weeks. Accelerating Ratecalorimetry (ARC) was used to measure the cells' self-heating rate attheir initial 100% state of charge (4.2 V). The faster the self-heatingrate, the lower the state of safety of the cell.

FIG. 37 provides data illustrating the differential entropy profile ofthe three cells. FIG. 38 provides data from the ARC experiments showingan increase in the self-heating rate for the 1 and 2 weeks aged cells.FIG. 39 illustrates data showing the self-heating peak intensity fromthe ARC experiments plotted as a function of differential entropy peakintensity at 5% SOC (corresponding to the anode). FIG. 40 illustratesdata showing the self-heating peak intensity from the ARC experimentsplotted as a function of differential entropy peak intensity at 80% SOC(corresponding to the cathode). The self-heating rate peak increaseswith the differential entropy at both 5 and 80% states of charge.Because the state of safety decreases with increasing self-heating rate,these data illustrate that the aging of the cells results in a lowerstate of safety, as determined using the ARC technique.

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Example 5 Thermodynamics of Lithium-Ion Batteries Introduction

In a series of journal articles [1-12], book example [13] and US patentapplications [14-20], we showed how thermodynamics techniques andmethods are useful to understand the behavior of anode [1,2,13,8,9,10],cathode [3,6,7,5,13] and full lithium-ion batteries (LiB) [11,12] duringcharge and discharge and during overcharge and thermal ageing. A LiBcell consists of an anode and a cathode, which reversibly incorporatelithium ions in their host structures <H>, following a general schematicequation:

<H>+xLi⁺

<Li_(x)H>  (1)

where ‘x’ is the electrode and/or the cell reaction advancement rate(0≦x≦1).

The change in the cell's free energy ΔG(x) relates to the cell'sopen-circuit potential (OCP), E₀(x) according to:

ΔG(x)=−nFE ₀(x)  (2)

where n=number of the transferred ions (here n=1 for Li⁺) andF=Faraday's constant.

The cell potential at equilibrium E₀(x) is given by:

E ₀(x)=E ₀ ⁺(x)−E ₀ ⁻(x)  (3)

where E₀ ⁺(x), E₀ ⁻(x) denote the cathode and anode potentials,respectively.

ΔG(x) also relates to changes in enthalpy ΔH(x) and entropy ΔS(x) atdefined electrode composition according to:

ΔG(x)=ΔH(x)−TΔS(x)  (4)

By deriving Eq. 2 vs. T at constant reaction advancement rate (x) andpressure (p) one obtains:

$\begin{matrix}{{\Delta \; {S(x)}} = {F( \frac{\partial{E_{0}( {x,T} )}}{\partial T} )}_{x,p}} & (5) \\{{\Delta \; {H(x)}} = {- {F( {{E_{0}( {x,T} )} + {T( \frac{\partial{E_{0}( {x,T} )}}{\partial T} )}_{x,p}} )}}} & (6)\end{matrix}$

(T=temperature; p=pressure)

According to Eqns. 5 and 6, the measurement of the temperaturedependence of E₀(x) at different x values enables ΔS(x) and ΔH(x) to beassessed and their profile to be plotted versus x and OCP (or E₀(x)). Wefound entropy and enthalpy profiles analysis to be particularly powerfulin revealing features at well-defined x and OCP values such as maximaand minima values, which can barely be detected in the OCP vs. xprofiles. The reason for such a higher detection capability is becauseboth ΔS(x) and ΔH(x) take into account the important thermodynamicparameter, temperature (T). Varying T by a few degrees enables revealingsubtle changes in the crystallographic and electronic structures of theelectrode materials according to their energy density of states. Sinceentropy is highly sensitive to disorder, it provides more detailedinformation on the changes taking place in the materials structureduring the cycling and ageing processes.

Configurational entropy, which is the dominating component of the totalentropy in chemical processes, besides vibrational and electronicentropy has a general expression:

S(x)=−k[x Ln x+(1−x)Ln(1−x)]  (7)

where k is the Boltzmann's constant.

The entropy variation ΔS(x) derives from Eq. 7 according to:

$\begin{matrix}{{\Delta \; {S(x)}} = {( \frac{\partial{S(x)}}{\partial x} )_{T,p} = {{- k}\; L\; n\frac{x}{1 - x}}}} & (8)\end{matrix}$

ΔS(x) should increase tremendously in absolute values at phasetransitions composition boundaries around x=0 and x=1. These transitionsare unique characteristics of electrode materials since they describetheir phase diagram. Accordingly, thermodynamics methods and techniquesturned out to be very efficient and nondestructive tools to characterizeelectrode materials phase diagram [13], cells chemistry [12, 13], stateof health [15], state of charge [16] and cycle history [21].

Most batteries are thermodynamically metastable because one or the twoelectrodes develop an electric potential which falls outside thepotential stability window of the electrolyte. This means that the anodeand/or the cathode should be oxidized and reduced by the electrolytemolecules, respectively. Still, batteries are stabilized for kineticsreasons as the electrode and electrolyte reactions are hindered bypassivation, considerably slowing their kinetics. For example the growthof a passivating solid electrolyte interphase (SEI) layer on thegraphite anode in LiB plays a major role in the battery chargeretention.

This Example is devoted to the thermodynamics characterization oflithium ion cells before and in the process of ageing. Three methodswere applied to accelerate the cells ageing:

(1) Overcharge up to 4.9 V as compared to the usual end of chargecut-off voltage (COV) of 4.2 V

(2) Thermal ageing: the cells are stored at 60° C. and 70° C. in theirinitial charged state at 4.2 V, and

(3) Galvanostatic cycling up to 1000 cycles under C/2-rate at ambienttemperature.

The entropy and enthalpy profiles evolution with ageing will bediscussed. We also show how thermodynamics allow to proactivelydetermining the kind of ageing mode batteries experienced and we willintroduce a new concept of LiB ageing memory effect.

Thermodynamics Measurements; Procedure and Equipment

LiB of coin cell form factor (2032), rated 44 mAh were used in thisstudy. Thermodynamics measurements were performed using a batteryanalyzer BA-1000® (produced by KVI PTE LTD, Singapore). BA-1000equipment displayed in FIG. 41 consists of three major parts:

(1) A temperature controlled battery holder capable of hosting up tofour cells,

(2) A potensiostat-galvanostat system with high accuracy potential andcurrent measurement capability, and

(3) A computer loaded with software to execute the thermodynamicsmeasurements steps, collect and process the data.

Regardless of the nature of the ageing mode, the protocol forthermodynamics measurements is the same. At first the cells weredischarged to 2.75 V then charged to 4.2 V followed by a seconddischarge to 2.75 V under a galvanostatic regime of 9 mA. During thisconditioning step, the BA-1000 assesses the cells' capacity q (mAh). Ina second phase thermodynamics measurements program starts stepwise. Ateach step, the state charge (SOC) is increased by 5% by applying aconstant current of C/6 (˜6 mA) for 30 minutes, followed by a potentialrest for 20 minutes during which the cells OCP rests to equilibrium. Thecells temperature is then decreased from ambient to about 10° C. by 5°C. increments. The temperature plateau is maintained for 20 minutesmeanwhile the OCP is monitored. After the last plateau at 10° C. iscompleted the temperature is left to reach the ambient then anadditional 5% SOC increment is applied. According to this procedure, atotal of twenty one OCP, entropy and enthalpy data are collected on eachcell during charge. Occasionally, at the end of charge of 4.2 V, athermodynamics measurements program is run during discharge undersimilar conditions as for charge, except a change in the current sign.For each thermodynamics measurements applied to four cells, we found theE₀(x), ΔS(x) and ΔH(x) profiles during charge and discharge almostidentical. Therefore, only the data during charge will be presented inthis Example.

Thermodynamics Data Before Ageing: Cell Chemistry Assessment

FIG. 42 shows the OCP vs. SOC profile of four fresh LiB cells. The OCPdata points fall on top of each other in the whole SOC range of 5%-100%proving excellent reproducibility. The only noticeable difference occursat SOC=0%. This may be due to small differences in lithium compositionin the graphite anode Li_(ε)C₆, ε˜0, where the anode potential variesconsiderably with E. A change in sign in the OCP curvature occurs aroundSOC of 55%.

FIG. 42 shows three OCP areas where the OCP profile has a differentbehavior: (a) 5%-25%; (b) 25%-55% and (c) 55%-100%. However, the OCPprofile is too smooth to allow for unequivocally identifying onsets ofphase transitions in the anode and cathode where the OCP is expected tomake a step or a plateau.

In contrast with the OCP profiles, entropy and enthalpy profilesdisplayed in FIG. 43 and FIG. 44, respectively show peaks, minima andchanges in slope. Several particular SOC values can be identified inboth ΔS and ΔH curves denoted A₁, A₂ and C₁ to C₅. These particular datapoints are associated with onsets of phase transitions in a graphiticanode (A₁, A₂) and in lithium cobalt oxide (LCO) cathode (from C₁ toC₅). In previous studies on Li/graphite and Li/LCO half cells [13], weattributed these particular data points to the following phasetransitions, schematically represented by the

sign:

A₁: graphite

dilute stage-1; i. e. Li_(ε)C₆ compound, ε˜0.05.

A₂: stage-2

stage-1 compound around x=0.5 in Li_(x)C₆.

C₁: one phase (O3I)″two phases (O3I+O3II) in LCO

C₂: two-phase hexagonal (O3I+O3II)

one-phase (O3II).

C₃: hexagonal one-phase (O3II)

monoclinic

C₄: monoclinic

O3II′

C₅: hexagonal (O3II′)

hexagonal (O3)

From the above and based on our nondestructive thermodynamics method, itcan be stated that the chemistry of the cells used in this studyconsists of a graphite anode and LCO cathode. The method can basicallyapply to any other battery more particularly LiB chemistry as phasetransitions and transformations in the anode and cathode provide acharacteristic fingerprint of each electrode material.

Thermodynamics of Overcharged Cells

Introduction

There are recommended ranges of cell' potential, temperature and chargeand discharge currents to insure the good operation of rechargeablebatteries. Outside these ranges, batteries undergo fast irreversibledegradation processes which accelerate their ageing. A cell ageingconverts to lower discharge capacity and discharge potentials and higherinternal resistances among others, which affects the cell' calendarlife.

Equation 3 gives the cell's potential at equilibrium E₀(x), i. e. atopen-circuit when no current flows in the cell. Under a charge anddischarge currents ‘i’ the cell potential E_(i) departs from E₀ owing toanode and cathode overpotentials, η_(a) and η_(c), respectively and toohmic drops R|i|.

E _(i) =E ₀±)|η_(a)|+|η_(c) |+R|i|)  (9)

(± sign is + during charge and − during discharge)

During the cell' overcharge, part of the irreversible energy −|η_(a)|Fand −|η_(c)|F may be used to overcome the activation energy of anode andcathode degradation, respectively and of electrolyte anodic oxidationand cathodic reduction reactions, which account for the cell'self-discharge and ageing [11, 22-25].

Overcharge Ageing Method

Cells were charged galvanostatically under a 10 mA rate up to a fixedcut-off voltage (COV) comprised between 4.2 V and 4.9 V. A constant COVplateau was then applied for 1 hour. For each set of tests four newcells were used and the COV is increased by 0.1 V. Accordingly differentcells were charged to 4.2V, 4.3V and so on up to 4.9V. The cells werethen discharged to 2.75 V and charged to 4.2 V followed by a dischargeto 2.75 V under 9 mA. The cells were then transferred to the BA-1000system to run a thermodynamics measurements test.

Discharge Characteristics

FIG. 45 shows discharge profiles of cells overcharged to different COVand the discharge results are displayed in Table 1, including dischargecapacity q_(d), capacity loss q_(CL), average discharge potential<e_(d)> and discharge energy output, E_(d)=q_(d)x<e_(d)>.

TABLE 1 Discharge data of LiB cells vs. end of charge cut off voltage(COV); q_(d), q_(CL), <e_(d)> and E_(d) refer to discharge capacity,discharge capacity loss, average discharge voltage and discharge energy,respectively. COV (V) q_(d) (mAh) q_(CL) (%) <e_(d)> (V) E_(d) (mWh) 4.243.07 0 3.82 164 4.3 42.51 1.30 3.81 162 4.4 41.44 3.78 3.80 157 4.540.62 5.69 3.78 153 4.6 38.09 11.56 3.77 143 4.7 37.35 13.28 3.76 1404.8 36.16 16.04 3.77 136 4.9 34.90 18.97 3.62 126

The cells incurred a large capacity loss between 4.5 V and 4.6 V COV,suggesting and important electrode and/or electrolyte materialsdegradation has taken place within this COV range.

We found an empirical relationship between capacity loss and COV with agood fit, which accounts for non-linearity:

q _(CL)(%)=35.47−40.12(COV)+7.56(COV)²  (10)

Moreover, a large drop in <e_(d)> occurs at COV of 4.9 V, perhaps due toa combined materials degradation and increase in the cell' internalresistance [11].

OCP Profiles

FIG. 46 displays the OCP vs. SOC profiles of overcharged cells. The OCPdata are more scattered than those in FIG. 42 before ageing. Datascattering is a sign of the overcharge effects on the cellsthermodynamics behavior. The OCP value at SOC=0 varies significantlywith the COV. This has been attributed to residual lithium in thegraphite anode and/or to lithium deficiencies in the LCO cathode [11].Above 5 SOC, slight differences appeared in the OCP profiles. However,there is no particular SOC value or range where significant OCP changescan be observed with increasing COV. Therefore, the OCP vs. SOC profilescannot be used to characterize cells aged at different COV with highlyenough resolution.

Entropy and Enthalpy Profiles

FIGS. 47 and 48 show the entropy and enthalpy profiles vs. SOC of cellsovercharged to different COV, respectively. FIGS. 49 and 50 show thesimilar data plotted vs. OCP, respectively. Entropy and enthalpyprofiles of FIGS. 47 and 48 show significant changes more particularlyin the following SOC domains: 0 to 5%, 40 to 65% and 65 to 90%. The dataat 80% SOC where both the entropy and enthalpy traces make a peak arestrongly COV dependent.

A large variation in entropy and enthalpy data may be used to bettercharacterize overcharged cells as compared to the OCP ones in FIG. 46.

We also found significant changes in the ΔS and ΔH data vs. OCP in FIGS.49 and 50 at OCP=3.87 V and OCP=3.94 V. Therefore, we have used theseparticular OCP values for accurate characterization of aged cells. Toachieve this task, cells were charged gavanostatically to 3.87 V (or3.94 V) then a potential plateau was applied at 3.87 V (or 3.94 V) untilthe current drops below C/100 (˜400 mA). Then a thermodynamics test wasrun to measure entropy and enthalpy around 3.87 V (or 3.94 V) OCPvalues.

FIG. 51 is a 3D (ΔS, ΔH, q_(CL)) plot of data achieved at OCP=3.87 V oncells overcharged to different COV. In fact, capacity loss q_(CL)increases with COV as displayed in Table 1 and in Equation 9.

FIG. 52 is the 2D projection of the q_(CL) trace of FIG. 51 on the (ΔS,ΔH) plan. As expected, all COV dependent q_(CL) data fall on the samestrait line since at constant OCP, ∂ΔH/∂ΔS is equal to T, which is theslope of the straight line of FIG. 52.

With increasing COV, the equipotential line drawn on the free energysurfaces takes different values making it possible to distinguishclearly between cells aged at different COV.

Similar results are obtained with OCP=3.94 V as displayed in FIGS. 53and 54 of the 3D and projected curves, respectively.

The reason why OCP values of 3.87 V and 3.94 V are so particular isbecause they are the actual potentials at which the graphite anode andthe LCO cathode undergo specific phase transitions, respectively.Particular OCP where changes in entropy and enthalpy are moresignificant are more sensitive to ageing, and accordingly, they can beused as metrics to assess the cell chemistry and its state of healthincluding during overcharge, allowing for a high resolution of the COVeffect on ageing to be achieved.

Thermodynamics of Thermally Aged Cells

Introduction

Thermal ageing is another well-known method to accelerate cells ageing[26-35]. Thermally activated electrode and electrolyte degradationprocesses, including irreversible phase transformations, electrodesurface passivation, electrode dissolution and precipitation andelectrolyte oxidoreduction account for most of the cell' self-dischargeand storage performance decays. In addition to temperature, the otherimportant controlling parameters of cell' ageing are the starting stateof charge and the state of health (calendar life). The higher is thestate of charge and the lower is the state of health, the faster is thecell ageing.

Thermal Ageing Method

Fresh cells were cycled between 2.75 V and 4.2 V at 10 mA (˜C/4 rate)for four cycles then cells were charged to 4.2 V and stored in an ovenat 60° C. and 70° C. for a period of time up to 8 weeks. At the end ofeach week, four cells were retrieved and tested by galvanostatic chargeand discharge and by thermodynamics measurements.

Discharge Characteristics

FIGS. 55A and 55B show the discharge profiles under a 10 mA rate ofcells aged at 60° C. and 70° C., respectively. Tables 2 and 3 summarizethe same discharge characteristics (q_(d), q_(CL), <e_(d)> and ε_(d)) asfunction of number of ageing weeks at 60° C. and 70° C., respectively.

TABLE 2 Discharge data of LiB cells aged at 60° C. vs. number of weeks;q_(d), q_(CL), <e_(d)> and E_(d) refer to discharge capacity, dischargecapacity loss, average discharge voltage and discharge energy,respectively. Weeks 60° C. q_(d) (mAh) q_(CL) (%) <e_(d)> (V) ε_(d)(mWh) 0 43.07 — 3.82 164 1 42.95 0.28 3.79 163 2 41.31 4.09 3.78 156 340.16 6.76 3.77 151 4 39.98 7.17 3.77 151 5 39.68 7.87 3.78 150 6 38.6510.26 3.76 145 7 37.66 12.56 3.75 141 8 36.88 14.37 3.72 137

TABLE 3 Weeks 70° C. q_(d) (mAh) q_(CL) (%) <e_(d)> (V) ε_(d) (mWh) 043.07 — 3.82 164 1 42.06 2.35 3.79 159 2 40.84 5.18 3.77 154 3 38.949.59 3.76 146 4 38.00 11.77 3.76 142 5 36.97 14.16 3.76 139 6 35.7716.95 3.75 134 7 34.93 18.90 3.74 131 8 32.65 24.19 3.73 122Discharge data of LiB cells aged at 70° C. vs. number of weeks; q_(d),q_(CL), <e_(d)> and E_(d) refer to discharge capacity, dischargecapacity loss, average discharge voltage and discharge energy,respectively.

The capacity loss after 8 weeks ageing is −14.4% and 24.2% at 60° C. and70° C., respectively. The average discharge potential <e_(d)> is not somuch affected by the ageing temperature. This observation supports themodel of active/less active electrode materials following which theanode and cathode discharge capacity and potentials under mild dischargerates are controlled by the active part still present in the electrodecomposition. The active part gradually converts to less active as cellsaged.

OCP Profiles

FIGS. 56A and 56B show the OCP vs. SOC profiles of cells aged for up to8 weeks at 60° C. and 70° C., respectively. At 60° C. the OCP profilesare not affected by the ageing time, whereas at 70° C., differences inOCP data appeared at SOC >55 as OCP decreases with ageing time. This isattributed to anode and cathode crystal structure degradation resultingfrom enhanced graphene layer disordering in the anode and the formationof spinel LCO phase in the cathode, both processes being thermallyactivated [12].

Entropy and Enthalpy Profiles

Entropy and enthalpy profiles of cells aged at 60° C. and 70° C. plottedvs. SOC are displayed in FIGS. 57A and 58A (60° C.) and FIGS. 57B and58B (70° C.), respectively. Entropy and enthalpy profiles plotted vs.OCP are shown in FIGS. 59A and 60A (60° C.) and FIGS. 59B and 60B (70°C.), respectively. As discussed in the section above, entropy andenthalpy profiles vs. SOC show more differences with ageing time at bothtemperatures of 60° C. and 70° C. as compared to OCP profiles. The SOCareas were differences in entropy and enthalpy are more noticeable are5%, 80 and 85%.

Here also we found entropy and enthalpy data at OCP of 3.87 V and 3.94 Vto show greater differences with ageing time. The 3D (ΔS, ΔH, q_(CL))profiles at 60° C. and 70° C. are shown in FIGS. 61A and 61B (3.87V),respectively and the corresponding projection in the (ΔS, ΔH) plan isdisplayed in FIGS. 62A and 62B (3.87 V) and FIGS. 63A and 63B (3D, 3.94V) and corresponding projection in FIGS. 64A and 64B (2D, 3.94V),respectively. The four projected plots show highly resolved ageing timedependence, enabling one to clearly distinguish between cells aged at60° C. and 70° C. for a determined period of time. The departure fromlinearity of the data in the curves at 3.87 V may denote a relativelylarge variation in the anode composition around this particularpotential and may be due to inherent uncertainty in the graphite anodecomposition and therefore its potential, which is not controlled in ourprocedure. Linearity, however, is quite well observed in the datacollected at 3.94 V of FIGS. 64A and 64B. As stated above 3.94V relatesto a phase transition in the LCO cathode. By comparing the entropy scalein FIGS. 64A and 64B it becomes obvious that the data are stronglyageing temperature dependent. Consequently, our thermal ageing studygives further support to the point that thermodynamics methods do allowdistinguishing between cells aged at different temperatures fordifferent durations of time.

Thermodynamics of Cycled Cells

Introduction

Long term cycling is the most natural ageing mode of rechargeablebatteries [36-39]. It results in both lower discharge potential andlower discharge capacity with increasing cycle number, ‘N’ [40-42] butalso with overdischarge [43] and as discussed above with overcharge[11,22-25] with charge and discharge rate [44-46].

Cell performances decay upon cycling results from the following causes:a) anode crystal structure degradation [47-49], b) cathode crystalstructure degradation [50-53], c) electrode/electrolyte interfaceproperties degradation [54-56]. d) metal dissolution [57-59], e)electrolyte decomposition [60-63], and f) surface film formation [63,64].

In this section LiB cells were cycled galvanostatically for up to 1000cycles and analyzed after each completed 100 cycles. We will report onthe cells discharge performance and on thermodynamics propertiesevolution upon cycle ageing.

Ageing Method

Four cells were cycled gavanostatically at 20 mA (˜C/2 rate) between2.75 V and 4.2 V at ambient temperature. After each completed 100cycles; the cells were analyzed by galvanostatic cycling and bythermodynamics methods. The same cells were then cycled again for anadditional 100 cycles until reaching 1000 cycles.

Discharge Characteristics

FIG. 65 shows the discharge profile after each completed 100 cycles andTable 4 displays the corresponding discharge characteristics. Capacityloss after 500 cycles and 1000 cycles is 20.4% and 35.6%, respectively.This converts to an average capacity loss rate of 0.094% per cycle.Moreover, we found that the cells' energy output decreases linearly withcycle number N according to:

E _(d)(N)(mWh)=133.6−0.0527×N  (11)

TABLE 4 Discharge data of LiB cells cycled up to 1000 cycles vs. cyclenumber; q_(d), q_(CL), <e_(d)> and E_(d) refer to discharge capacity,discharge capacity loss, average discharge voltage and discharge energy,respectively. Cycle number q_(d)(mAh) q_(CL) (%) <e_(d)> (V) E_(d) (mWh)1 36.58 — 3.72 136 100 34.28 6.3 3.73 128 200 32.92 10 3.72 122 30031.78 13.1 3.68 117 400 30.75 15.9 3.67 113 500 29.11 20.4 3.65 106 60028.10 23.2 3.65 103 700 25.99 28.9 3.65 95 800 25.19 31.1 3.58 90 90024.40 33.3 3.56 87 1000 23.55 35.62 3.54 83

OCP Profiles

FIG. 66 shows the OCP vs. SOC profiles of cells aged N=100n cycles(n=1-10), together with a fresh cell (N=1). The OCP vs. SOC data pointslay on top of each other indicating no significant effect of cycling onOCP vs. SOC profiles has taken place. Since the discharge capacity andthe discharge potential decreased with the cycle number, the OCP resultssuggest the galvanostatic cycling gradually converts active anode andcathode material into less active material. The conversion of activeinto less active (or inactive) material upon ageing does not affect muchthe corresponding electrode potential as function of the SOC, since thelater normalizes the active material to 100%.

Entropy and Enthalpy Profiles

FIGS. 67 and 68 show the entropy and enthalpy profiles vs. SOC atdifferent N values, respectively. The corresponding entropy and enthalpycurves traced vs. OCP are displayed in FIGS. 69 and 70, respectively.

Similarly to the previous sections 3D (ΔS, ΔH, q_(CL))) and projectioncurves at OCP=3.87 V and 3.94 V are showed in FIGS. 71 and 72 (OCP=3.87V) and in FIGS. 73 and 74 (OCP=3.94 V), respectively.

FIGS. 72 and 74 show a good alignment of the data points projected onthe (ΔS, ΔH) plan. This is particularly true in FIG. 72 of datacollected at 3.87 V suggesting a good sensitivity of thermodynamics tochanges in the graphite anode, although we found that the graphitestructure is not much affected by cycling. We also found by ex-situanalyses using XRD and Raman scattering that, surprisingly, the graphitecrystal structure improved upon cycling [21].

In contrast, FIG. 74 of data points collected at 3.94 V show excellentresolution with regards to N. This opens for a new application ofthermodynamics as a tool to assess cells cycle number.

The difference in data resolution at 3.87 V and 3.94 V comes from thefact that the LCO cathode controls the cell capacity fading duringgalvanostatic cycling at ambient temperature. This statement wassupported by post-mortem XRD and Raman scattering analyses performed onthe graphite anode and LCO cathode, which unambiguously showed little,if any, changes in the graphite crystal structure after 1000 cycles,whereas by contrast, the LCO cathode structure was strongly affected byextended cycling [21,49-51]. Therefore, thermodynamics data collected at3.94 V, which relate to a phase transition in the LCO cathode, areexpected to exhibit more significant changes with the cycle number ascompared to those collected at 3.87 V relating to the graphite anode.

Thermodynamics Memory Effect

In the previous sections on LiB ageing we showed how thermodynamicstechniques are affective in assessing 1) the COV of overchargedbatteries, 2) the duration of thermal ageing, and 3) the cycle number ofaged cells. In this section we will attempt to address the questionwhether a LiB keeps memory of the kind of ageing process that lead to acertain capacity fade. To achieve this task, we selected among the fourageing methods presented in this Example the conditions leading to thesame capacity loss of the cells such as q_(u), of 5%, 10%, 15%, 20% and25%. The corresponding ageing conditions are exhibited in Table 5.

TABLE 5 Ageing conditions under which LiB cells incurred a capacity lossof 5% to 25%. Capacity loss (%) Overcharge Thermal Cycling 5 4.5 V 60°C., 3 Weeks 100 70° C., 2 Weeks 10 4.6 V 60° C., 6 Weeks 300 70° C., 4Weeks 15 4.8 V 60° C., 8 Weeks 400 70° C., 6 Weeks 20 4.9 V 70° C., 7Weeks 500 25 — 70° C., 8 Weeks 600

FIGS. 75 to 79 show the coordinates location of the data points in the(ΔS, ΔH) plan corresponding to the ageing conditions which led to 5% to25% capacity loss, respectively. The thermodynamics data showed in FIGS.75 (5%), 76 (10%) 77 (15%), 78 (20%) and 79 (25%) are collected at cellsOCP value of 3.94 V. We can see that the data points in FIGS. 75 to 79are quite well scattered, except in FIG. 75 where the data points after3 weeks ageing at 60° C. and 2 weeks at 70° C. are too close to make anyunambiguous distinction between them.

Accordingly, our new thermodynamics methods do allow for clearrecognition of the nature of the ageing mode together with the ageingconditions a LiB cell has experienced. To the authors knowledge this isthe first time such a battery history or ageing memory has been unveiled[20].

Conclusion

New approaches of thermodynamics studies of LiB before and after ageinghave been presented and discussed in this Example. We believe asignificant contribution of this work resides in the fact that thethermodynamics path taken by a battery system strongly depend on theageing conditions. Batteries keep traces or a memory of these ageingconditions, which have been unveiled for the first time usingthermodynamics methods. In particular, for LiB consisting of graphiteanode and LCO cathode, we found two particular OCP were the changes inentropy and enthalpy are more pronounced. At OCP of 3.87 V informationon changes in the graphite anode upon ageing can be obtained whereas atOCP=3.94 V those on the LCO cathode are concerned. Accordingly, bydriving the potential of a LiB cell based on graphite anode and LCOcathode to 3.87 V and 3.94 V and changing the cell' temperature andmonitoring the OCP vs. T, one can determine entropy and enthalpy atthose particular OCP values and plot the data in the ΔS, ΔH plan, thusunveiling the cell's SOC, capacity loss and ageing mode usingcalibration curves presented here. For other LiB chemistries a studywould be beneficial to uncover the particular cell potentials ofinterest which enable resolving the effect of ageing according to ageingparameters such as T, time, COV and N.

Certain merits of thermodynamics measurements methods are summarized asfollows:

(1) non-destructiveness (in-situ measurements),

(2) universality as they can apply to any primary and rechargeablebattery chemistry, including alkaline and high temperature cells.

(3) high resolution in potential and SOC onsets assessment of phasetransitions in half-cells and full-cells.

(4) versatility of applications such as in cells chemistry, SOC, SOH,SOS and ageing memory diagnosis,

(5) high reproducibility, and

(6) cost effectiveness compared to other techniques based on in-situ orex-situ diffractometry and physical spectrometry.

These results demonstrate that unveiling the battery ageing history andmemory through thermodynamics is a breakthrough in the battery scienceand technology.

TERMINOLOGY Abbreviations

2D Two dimensional

3D Three dimensional

COV End of charge cut-off voltage

LCO Lithium cobalt oxide

LiB Lithium ion batteries

OCP Open-circuit potential

SEI Solid electrolyte interphase

SOC State of charge

SOD State of discharge

SOH State of health

SOS State of safety

US United States of America

XRD X-ray diffractometry

Roman

A, mA Ampere, milliampere

A₁, A₂ Onsets of phase transition in the graphite anode

BA-1000 Battery Analyzer for thermodynamics measurements

C Carbon

° C. Degrees centigrade

C₁ to C₅ Onsets of phase transitions in the LCO cathode

C/n C-rate (mA)

E₀, E₀(x) Open-circuit potential (V)

E₀ ⁺ Cathode potential (V)

E₀ ⁻ Anode potential (V)

E_(i) Cell potential under current I (V)

<e_(d)> Average discharge potential (V)

ε_(d) Discharge energy (mWh)

F Faraday′ constant (C)

G Free (Gibbs) energy (J mole⁻¹)

H Electrode host structure

H Enthalpy (kJ mole⁻¹)

i Electric current intensity (mA)

k Boltzmann′ constant (JK⁻¹ mole⁻¹)

Li Lithium

n Charge number

n index number

N Cycle number

O3 Hexagonal phases in LCO

p Pressure (Atm)

q_(d) Discharge capacity (mAh)

q_(CL) Capacity loss (%)

R Ohmic resistance

S Entropy (JK⁻¹ mole⁻¹)

t Ageing time (weeks)

T Absolute temperature (K)

T Ageing temperature (° C.)

V Volt

x Cell reaction advancement rate

x Fraction of the occupied sites by lithium

Greek

ΔG Change in Gibbs energy (J mole⁻¹)

ΔH Change in enthalpy (J mole⁻¹)

ΔS Change in entropy (JK⁻¹ mole⁻¹)

ε Li composition in LiεC₆

η_(a) Anodic overpotential (V)

η_(c) Cathodic overpotential (V)

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Ogumi;    Electrochim. Acta 78 (2012) 49

Example 6 Accurate Assessment of the State of Charge (SOC) of LithiumIon Batteries

Three principals for the accurate assessment of the state of charge oflithium ion batteries are: (1) Thermodynamics data (ΔS and ΔH) arecomputed during charge and discharge of lithium ion batteries (LIBs)using conventional thermodynamics equations:

${\Delta \; {S(x)}} = {F\frac{\partial{E_{0}(x)}}{\partial T}}$${\Delta \; {H(x)}} = {- {F( {E_{0} + {T\frac{\partial{E_{0}(x)}}{\partial T}}} )}}$

(2) LIBs were aged by means of high temperature storage at initialcharged state at 4.2V for up to 8 weeks and high voltage charge from4.3V to 4.9V instead of to normal 4.2V and (3) 3 (ΔS, ΔH, SOC)multidimensional state of charge profiles were plotted, which allowshigh resolution SOC assessment to be achieved compared to OCV curves.

Results are presented in FIGS. 80-95. FIG. 80 provides a 3D profile ofLIB before ageing. FIG. 81 provides OCV Profiles at various aging points(in weeks) at 60° C. FIG. 82 provides a 3D profile of a 2 week aged cellat 60° C. FIG. 83 provides a 3D profile of an 8 week aged cell at 60° C.FIG. 84 provides projected curves (w/SOC). FIG. 85 provides OCV Profilesat various aging points (in weeks) at 70° C. FIG. 86 provides 3D of 2week aged cell at 70° C. FIG. 87 provides 3D of 8 week aged cell at 70°C. FIG. 88 provides projected curves w/SOC. FIG. 89 provides a 3Dprofile of charged cell to 4.2V. FIG. 90 provides a 3D profile ofovercharged cell to 4.6V. FIG. 91 provides a 3D of overcharged cell to4.9V. FIG. 92 provides projected curves w/SOC. FIG. 93 provides Entropyand Enthalpy vs. normalized SOC of LIBs upon cycling. FIG. 94 providesEntropy and Enthalpy vs. OCV of LIBs upon cycling. FIG. 95 provides ΔSand ΔH vs. OCV of a Graphite Anode.

In some embodiment, the new method based on thermodynamics measurementsallows a higher resolution in the SOC assessment than the one basedsoley on OCV measurements. The new methods are easily digitalized owingto an integrated circuit that collects cell's temperature and voltage inreal time to convert them to thermodynamics data and then to SOC data.

In some systems, the state of charge (SOC) of a battery relates to theamount of available discharge capacity (Ah). In some embodiments, forexample, the SOC relates to the amount of ions potentially exchangeablebetween anode and cathode during discharge. In some embodiments, forexample, the SOC of the battery is fixed by the limiting electrode, i.e. the one that has the lowest amount of available ions for the exchangewith the other electrode. Thermodynamics data allow to determineprecisely the state of charge of each electrode at which phasetransitions take place. These transitions can be used as markers (ormilestones) to determine the SOC of each electrode and therefore the SOCof the full cell.

Example 7 Imbedded Chip for Battery Application

1. Introduction

This example describes an integrated circuit for online analysis ofbattery states of charge, health and safety. We have designed and testedan Integrated Circuit (IC) board connected to a PC for online batterystate of charge (SOC), state of health (SOH) and state of safety (SOS)assessment. Further we have developed software to convert IC data tothermodynamics then to SOC, SOH and SOS. We then collectedthermodynamics data with BA 2000 on different LIB cells in two states(a) Fresh (100% SOH) and (b) Aged (<100% SOH) Then compare data acquiredwith BA 2000 and with the IC.

The integrated circuit in FIG. 96 uses a chip from Freescale (PreviousMotorola) KL25 microcontroller and has the following attributes:

16-bit ADC

Processing capabilities

Temperature sensors connections

Chip′ specifications

Temperature resolution <0.1° C.

Voltage resolution <0.1 mV

Time acquisition <10 s

Processing capability

Radio feature

2. Experimental Procedure

Step 1: A prismatic lithium ion battery from Energizer (rated 610 mAh)was first scanned with BA 2000. Entropy, enthalpy and OCV profiles wereacquired and used as reference.

Step 2: The same battery taken at three different unknown states ofcharge (SOC) was mounted in the IC. The IC attached to a laptop PC wastransferred outside the lab. into another room in the same building.Temperature and voltage were monitored during the transfer which takes afew minutes

Step 3: Entropy and enthalpy were calculated from the voltage vs.temperature profiles during transfer. Data were compared to referencecurves of step 1 and SOC was determined.

ETM data on commercial LIB (Using BA 2000):

1. LG 2600—Data presented in FIGS. 109-112.2. LG 3200—Data presented in FIGS. 113-116.3. Sony 2600—Data presented in FIGS. 117-204. Samsung 2500—Data presented in FIGS. 121-1245. Panasonic 3400—Data presented in FIGS. 125-28The thermodynamic parameters of the Sony 3600, LG 3200 and SONY 2600 arecompared in FIGS. 129 and 130.

Example 8 Multidimensional State of Charge Profile

This example provides two exemplary ways to generate multidimensionalstate of charge profile:

Controlled generation: In this method the cell' SOC is changed(increased during charge or decreased during discharge) stepwise. Foreach step ‘k’ the SOC is incremented by d(SOC)_(k) so asSOC(k+1)=SOC(k)±d(SOC)_(k), 1≦k≦n, n=total number of steps. d(SOC)_(k)can be constant(x % for instance), in which case

$n = {\frac{100}{x}.}$

For instance we can apply a constant current ‘i’ for a constant periodof time dt, so as d(SOC)_(k) is proportional to idt. (d(SOC)_(k)μidt),or alternately, d(SOC)_(k) can also be variable according to aprogrammed schedule.

Uncontrolled generation: here the cell is charging or dischargingintermittently. Each time the cell is at rest (no current is flowing(i=0), such as when an electric car is stopped at traffic light orparking, or a cellphone/laptop PC is in sleep mode of shutoff), theopen-circuit voltage is recorded vs. temperature generatingthermodynamics data; which are then be recorded. Over time, amultidimensional state of charge profile is generated.

Upon ageing, the cell' entropy and enthalpy profiles will change. Thesechanges in profile were found to be strongly related to the ageing modeof the cell (cycle ageing, thermal ageing, overcharge ageing, . . . ),therefore, teaching on the ageing memory of the cell. Of course state ofhealth and state of safety can also be derived from the multidimensionalstate of charge profile.

Example 9 Functionality of State of Charge Profiles

Using a chip with the required resolution to measure entropy accurately,another aspect may be considered: i. e. the measurement time. In fact,measurements as they are performed currently take three to four days fora complete entropy profile. When the current is switch off at a definedSOC, the lead time for voltage relaxation to reach OCP could be hours,depending on SOC, capacity, chemistry, etc.

In this example we describe methods for predicting OCP within minutes bysimulating OCP relaxation with mathematical equations found in theliterature [3-5]. Since OCP and entropy are related via temperature, themodel should also include temperature as parameter.

Three models have been considered. The OCP prediction for the relaxationpart of those models comes from literature. Then a term which isdependent on temperature and Entropy has been added.

Following are the three models expressions:

Model 1:

V_(Bat) = A e^(−t/τ_(d)(t)) + OCV(T) τ_(d)(t) = α t + β${{OCV}(T)} = {{\frac{\Delta \; S}{F}T} + B}$

wherein V_(Bat) is relaxation terminal voltage, t is time, T istemperature, OCP is open circuit potential, ΔS is entropy, F is theFaraday constant and ΔS, A, B, α and β are constants which aredetermined.

Model 2:

$V_{Bat} = {{\frac{\Gamma}{t^{\alpha}l\; {n^{\beta}(t)}}e^{\gamma/2}} + {{OCV}\; (T)}}$${{EFM}(T)} = {{\frac{\Delta \; S}{F}T} + B}$

wherein V_(Bat) is relaxation terminal voltage, t is time, T istemperature, OCP is open circuit potential, ΔS is entropy, F is theFaraday constant, Γ is −1 after discharge and +1 after charge, and ΔS,α, β and γ are constants which are determined.

Model 3:

$V_{Bat} = {\frac{{A\; t} + B}{t^{2} + {Ct} + D} + {{OCV}(T)}}$${{OCV}(T)} = {{\frac{\Delta \; S}{F}T} + E}$

wherein V_(Bat) is relaxation terminal voltage, t is time, T istemperature, OCP is open circuit potential, ΔS is entropy, F is theFaraday constant, Γ is −1 after discharge and +1 after charge, and A, B,C, D and E are constants which are determined.

We applied each model to the relaxation voltage after the current isswitched off on a 3 Ah 18650 cell from Panasonic. The models agree verywell with the measured voltages. To show more on the models validity, wemade a zoom of FIG. 131 and added the temperature variation on the graphas shown in FIG. 132. Here again the models follow very well themeasured relaxation voltage. One important remark is that the voltagevariation due to relaxation is comparable to the one due to temperaturevariation. This reinforces the need of a fit. In fact, the models takeinto account the drift to get an accurate entropy value.

Levenberg-Marquardt algorithm is used to determine the modelsparameters. The fit has been done at every 5% SOC on the relaxationvoltage for the three models. FIG. 133 is a plot of errors. 0% SOC isnot significant, therefore it is discarded. At 55% the fit is relativelyless good than the other states of charge. It seems that significantchanges take place in the cell structure at 55% SOC, so it is difficultto model very well the relaxation. We also noted that model 3 gives lesserror for these systems.

By doing this regression we obtain entropy values for each state ofcharge. FIG. 134 shows those values for the three models and the onemeasured by the BA2000. The entropy computed from the regression and theone computed with the BA2000 are very close. We can notice a differenceat 55% which may be explained if the fit or the drift is not wellcorrected by the BA 2000. It may also come from a phase transitiontaking place in anode or cathode at 55% SOC.

The results of this example demonstrate that the models chosen describevery well the relaxation process.

STATEMENTS REGARDING INCORPORATION BY REFERENCE AND VARIATIONS

The following references relate generally to the composition andfunction of electrochemical cells and the thermodynamic analysis ofelectrochemical data and are incorporated by reference in theirentireties herein: Handbook of Batteries, Edited by David Linden andThomas B. Reddy, Third Edition, McGraw-Hill, 2002; and BatteryTechnology Handbook, Edited by H. A. Kiehne, Marcel Dekker, Inc., 2003.

All references throughout this application, for example patent documentsincluding issued or granted patents or equivalents; patent applicationpublications; and non-patent literature documents or other sourcematerial; are hereby incorporated by reference herein in theirentireties, as though individually incorporated by reference, to theextent each reference is at least partially not inconsistent with thedisclosure in this application (for example, a reference that ispartially inconsistent is incorporated by reference except for thepartially inconsistent portion of the reference).

The following patents, patent applications and publications are herebyincorporated by reference in their entireties: U.S. application Ser.Nos. 11/462,290, 12/537,712, 13/215,506; U.S. Provisional Applications60/705,535, 61/159,727, 61/639,712, 61/260,751, 61/376,208, 61/556,037,61/726,459, 61/536,239; U.S. Pat. No. 7,595,611; US Patent ApplicationPublications US 2007/0182418, US 2010/0090650, US 2012/0043929.

All patents and publications mentioned in the specification areindicative of the levels of skill of those skilled in the art to whichthe invention pertains. References cited herein are incorporated byreference herein in their entirety to indicate the state of the art, insome cases as of their filing date, and it is intended that thisinformation can be employed herein, if needed, to exclude (for example,to disclaim) specific embodiments that are in the prior art. Forexample, when a compound is claimed, it should be understood thatcompounds known in the prior art, including certain compounds disclosedin the references disclosed herein (particularly in referenced patentdocuments), are not intended to be included in the claim.

When a group of substituents is disclosed herein, it is understood thatall individual members of that group and all subgroups, including anyisomers, enantiomers, and diastereomers of the group members, aredisclosed separately. When a Markush group or other grouping is usedherein, all individual members of the group and all combinations andsubcombinations possible of the group are intended to be individuallyincluded in the disclosure. When a compound is described herein suchthat a particular isomer, enantiomer or diastereomer of the compound isnot specified, for example, in a formula or in a chemical name, thatdescription is intended to include each isomers and enantiomer of thecompound described individual or in any combination. Additionally,unless otherwise specified, all isotopic variants of compounds disclosedherein are intended to be encompassed by the disclosure. For example, itwill be understood that any one or more hydrogens in a moleculedisclosed can be replaced with deuterium or tritium. Isotopic variantsof a molecule are generally useful as standards in assays for themolecule and in chemical and biological research related to the moleculeor its use. Methods for making such isotopic variants are known in theart. Specific names of compounds are intended to be exemplary, as it isknown that one of ordinary skill in the art can name the same compoundsdifferently.

It must be noted that as used herein and in the appended claims, thesingular forms “a”, “an”, and “the” include plural reference unless thecontext clearly dictates otherwise. Thus, for example, reference to “acell” includes a plurality of such cells and equivalents thereof knownto those skilled in the art, and so forth. As well, the terms “a” (or“an”), “one or more” and “at least one” can be used interchangeablyherein. It is also to be noted that the terms “comprising”, “including”,and “having” can be used interchangeably. The expression “of any ofclaims XX-YY” (wherein XX and YY refer to claim numbers) is intended toprovide a multiple dependent claim in the alternative form, and in someembodiments is interchangeable with the expression “as in any one ofclaims XX-YY.”

Unless defined otherwise, all technical and scientific terms used hereinhave the same meanings as commonly understood by one of ordinary skillin the art to which this invention belongs. Although any methods andmaterials similar or equivalent to those described herein can be used inthe practice or testing of the present invention, the preferred methodsand materials are now described. Nothing herein is to be construed as anadmission that the invention is not entitled to antedate such disclosureby virtue of prior invention.

Every formulation or combination of components described or exemplifiedcan be used to practice the invention, unless otherwise stated. Specificnames of materials are intended to be exemplary, as it is known that oneof ordinary skill in the art can name the same material differently. Oneof ordinary skill in the art will appreciate that methods, deviceelements, starting materials, and synthetic methods other than thosespecifically exemplified can be employed in the practice of theinvention without resort to undue experimentation. All art-knownfunctional equivalents, of any such methods, device elements, startingmaterials, and synthetic methods are intended to be included in thisinvention. Whenever a range is given in the specification, for example,a temperature range, a time range, or a composition range, allintermediate ranges and subranges, as well as all individual valuesincluded in the ranges given are intended to be included in thedisclosure.

As used herein, “comprising” is synonymous with “including,”“containing,” or “characterized by,” and is inclusive or open-ended anddoes not exclude additional, unrecited elements or method steps. As usedherein, “consisting of” excludes any element, step, or ingredient notspecified in the claim element. As used herein, “consisting essentiallyof” does not exclude materials or steps that do not materially affectthe basic and novel characteristics of the claim. Any recitation hereinof the term “comprising”, particularly in a description of components ofa composition or in a description of elements of a device, is understoodto encompass those compositions and methods consisting essentially ofand consisting of the recited components or elements. The inventionillustratively described herein suitably may be practiced in the absenceof any element or elements, limitation or limitations which is notspecifically disclosed herein.

Whenever a range is given in the specification, for example, atemperature range, a time range, or a composition or concentrationrange, all intermediate ranges and subranges, as well as all individualvalues included in the ranges given are intended to be included in thedisclosure. As used herein, ranges specifically include the valuesprovided as endpoint values of the range. For example, a range of 1 to100 specifically includes the end point values of 1 and 100. It will beunderstood that any subranges or individual values in a range orsubrange that are included in the description herein can be excludedfrom the claims herein.

As used herein, “comprising” is synonymous with “including,”“containing,” or “characterized by,” and is inclusive or open-ended anddoes not exclude additional, unrecited elements or method steps. As usedherein, “consisting of” excludes any element, step, or ingredient notspecified in the claim element. As used herein, “consisting essentiallyof” does not exclude materials or steps that do not materially affectthe basic and novel characteristics of the claim. In each instanceherein any of the terms “comprising”, “consisting essentially of” and“consisting of” may be replaced with either of the other two terms. Theinvention illustratively described herein suitably may be practiced inthe absence of any element or elements, limitation or limitations whichis not specifically disclosed herein.

One of ordinary skill in the art will appreciate that startingmaterials, biological materials, reagents, synthetic methods,purification methods, analytical methods, assay methods, and biologicalmethods other than those specifically exemplified can be employed in thepractice of the invention without resort to undue experimentation. Allart-known functional equivalents, of any such materials and methods areintended to be included in this invention. The terms and expressionswhich have been employed are used as terms of description and not oflimitation, and there is no intention that in the use of such terms andexpressions of excluding any equivalents of the features shown anddescribed or portions thereof, but it is recognized that variousmodifications are possible within the scope of the invention claimed.Thus, it should be understood that although the present invention hasbeen specifically disclosed by preferred embodiments and optionalfeatures, modification and variation of the concepts herein disclosedmay be resorted to by those skilled in the art, and that suchmodifications and variations are considered to be within the scope ofthis invention as defined by the appended claims.

The terms and expressions which have been employed herein are used asterms of description and not of limitation, and there is no intention inthe use of such terms and expressions of excluding any equivalents ofthe features shown and described or portions thereof, but it isrecognized that various modifications are possible within the scope ofthe invention claimed. Thus, it should be understood that although thepresent invention has been specifically disclosed by preferredembodiments, exemplary embodiments and optional features, modificationand variation of the concepts herein disclosed may be resorted to bythose skilled in the art, and that such modifications and variations areconsidered to be within the scope of this invention as defined by theappended claims. The specific embodiments provided herein are examplesof useful embodiments of the present invention and it will be apparentto one skilled in the art that the present invention may be carried outusing a large number of variations of the devices, device components,methods steps set forth in the present description. As will be obviousto one of skill in the art, methods and devices useful for the presentmethods can include a large number of optional composition andprocessing elements and steps.

1. A method for characterizing the state of charge of an electrochemicalcell, said method comprising the steps of: generating a multidimensionalstate of charge profile corresponding to said electrochemical cell;measuring a plurality of open circuit voltages of said electrochemicalcell corresponding to a plurality of temperatures of saidelectrochemical cell; determining a plurality of thermodynamicparameters corresponding to said electrochemical cell, wherein saidthermodynamic parameters are selected from the group comprising: achange in enthalpy (ΔH), a change in entropy (ΔS) and a change in freeenergy (ΔG); and characterizing said state of charge of saidelectrochemical cell using said multidimensional state of charge profileand said thermodynamic parameters. 2-3. (canceled)
 4. The method ofclaim 1, comprising measuring said plurality of temperatures of saidelectrochemical cell.
 5. The method of claim 1, wherein saidmultidimensional state of charge profile is defined by at least threevariables.
 6. (canceled)
 7. The method of claim 5, wherein saidmultidimensional state of charge profile is a nonlinear functionrelating state of charge to change in enthalpy (ΔH) and change inentropy (ΔS).
 8. The method of claim 5, wherein characterizing saidstate of charge of said electrochemical cell comprises comparing achange in enthalpy (ΔH) and a change in entropy (ΔS) determined for saidelectrochemical cell to said multidimensional state of charge profile todetermine said state of charge of said electrochemical cell.
 9. Themethod of claim 5, wherein characterizing said state of charge of saidelectrochemical cell comprises identifying the state of chargecorresponding to a change in enthalpy (ΔH) and a change in entropy (ΔS)determined for said electrochemical cell for said multidimensional stateof charge profile.
 10. The method of claim 1, wherein said step ofgenerating a multidimensional state of charge profile comprises:generating a plurality of different states of charge for saidelectrochemical cell; and measuring said thermodynamic parameterscorresponding to each of said plurality of states of charge; whereinsaid thermodynamic parameters are selected from the group comprising: achange in enthalpy (ΔH), a change in entropy (ΔS) and a change in freeenergy (ΔG), thereby generating said multidimensional state of chargeprofile.
 11. The method of claim 10, wherein said step of generating aplurality of states of charge is carried out stepwise by increasing ordecreasing said state of charge of said electrochemical cell. 12.(canceled)
 13. The method of claim 10, wherein said plurality of statesof charge are measured using a charge calculating circuit. 14.(canceled)
 15. The method of claim 1, further comprising selectivelyadjusting the temperature said electrochemical cell so as to establishsaid plurality of temperatures of said electrochemical cell.
 16. Themethod of claim 1, wherein said plurality of temperatures of saidelectrochemical cell are established by in situ temperatures changes ofsaid electrochemical cell during use.
 17. The method of claim 1, whereinsaid open circuit voltages of said electrochemical cell are eachindependently measured to a margin of error less than or equal to 0.01mV and wherein said temperatures of said electrochemical cell areindependently measured to a margin of error less than or equal to 0.01K.
 18. (canceled)
 19. The method of claim 1, wherein said open circuitvoltages of said electrochemical cell independently correspond tothermochemically stabilized conditions.
 20. The method of claim 19,wherein said step of measuring a plurality of open circuit voltagescomprises independently determining a plurality of observed rates ofchange in open circuit voltage per unit time for each correspondingtemperature.
 21. The method of claim 20, wherein an absolute value ofsaid change in open circuit voltage per unit time is compared to athreshold open circuit voltage per unit time corresponding to saidtemperature, wherein said thermochemically stabilized conditionscorrespond to conditions of said absolute value of said change in opencircuit voltage per unit time less than said threshold open circuitvoltage per unit time.
 22. The method of claim 21, wherein saidthreshold open circuit voltage per unit time in open circuit voltage perunit time is less than or equal to 1.0 mV h⁻¹. 23-24. (canceled)
 25. Themethod of claim 1, further comprising determining a state of health ofsaid electrochemical cell using said state of charge determined for saidelectrochemical cell, wherein said state of health is determined bycomparing said determined state of charge with a threshold state ofcharge, wherein said threshold state of charge is a maximum state ofcharge from an electrochemical cell provided in a new condition. 26.(canceled)
 27. The method of claim 1, further comprising determining astate of safety of said electrochemical cell using said state of chargedetermined for said electrochemical cell, wherein said state of safetyis determined by using said state of charge and said temperature tocalculate the probability of a thermal runaway corresponding to saidelectrochemical cell, wherein said state of safety is a function of theprobability of a thermal runaway.
 28. (canceled)
 29. A measurementsystem for thermodynamically characterizing a state of charge of anelectrochemical cell; said system comprising: a temperature analyzer formeasuring or receiving temperature measurements of said electrochemicalcell; an open circuit voltage analyzer for measuring open circuitvoltages corresponding to a plurality of different temperatures of saidelectrochemical cell; a thermodynamic parameter processor positioned indata communication with said temperature analyzer and said open circuitvoltage analyzer, said processor programmed to determine thermodynamicparameters based on said open circuit voltage measurements and saidtemperature measurements; wherein said thermodynamic parameters areselected from the group comprising: a change in enthalpy (ΔH), a changein entropy (ΔS) and a change in free energy (ΔG); and a state of chargeprocessor positioned in data communication with said temperatureanalyzer and said open circuit voltage analyzer, said processorprogrammed to characterize said state of charge of said electrochemicalcell using said plurality of said thermodynamic parameters and amultidimensional state of charge profile. 30-31. (canceled)
 32. Themeasurement system of claim 29, further comprising a current analyzerfor measuring charging and discharging current for characterizing saidmultidimensional state of charge profile corresponding to saidelectrochemical cell. 33-34. (canceled)
 35. The measurement system ofclaim 29, wherein said multidimensional state of charge profile is anonlinear function relating state of charge to change in enthalpy (ΔH)and change in entropy (ΔS).
 36. The measurement system of claim 29,wherein said processor characterizes said state of charge of saidelectrochemical cell by comparing or identifying a change in enthalpy(ΔH) and a change in entropy (ΔS) determined for said electrochemicalcell to said multidimensional state of charge profile to determine saidstate of charge of said electrochemical cell. 37-39. (canceled)
 40. Themeasurement system of claim 29, wherein said system is positioned inselective data or selective electrical communication with one or moreelectrochemical cells; or wherein said device is positioned inswitchable data communication or switchable electrical communicationwith one or more electrochemical cells; or wherein said system is inwireless data communication or wireless electrical communication withsaid electrochemical cell.
 41. (canceled)
 42. The measurement system ofclaim 29, wherein said processor programmed to determine thermodynamicparameters and said processor programmed to characterize state of chargeare a single processor and wherein said measurement system is anintegrated circuit. 43-44. (canceled)
 45. The measurement system ofclaim 29 further comprising a current controller wherein said currentcontroller generates a plurality of different states of charge for saidelectrochemical cell and said processor measures said thermodynamicparameters corresponding to each of said plurality of said states ofcharge and generates a multidimensional state of charge profile whereinsaid current controller generates a plurality of states of charge bystepwise increasing or decreasing said state of charge of saidelectrochemical cell. 46-48. (canceled)
 49. The measurement system ofclaim 29, wherein said open circuit voltage analyzer measures opencircuit voltages corresponding to thermochemically stabilizedconditions.
 50. The measurement system of claim 29, wherein said opencircuit voltage analyzer independently measures rates of change in opencircuit voltage per unit time for each corresponding temperature and anabsolute value of said change in open circuit voltage per unit time iscompared to a threshold open circuit voltage per unit time correspondingto said temperature, wherein said thermochemically stabilized conditionscorrespond to conditions of said absolute value of said change in opencircuit voltage per unit time less than said threshold open circuitvoltage per unit time. 51-59. (canceled)
 60. A device for monitoring thestate of charge of an electrochemical cell, said device comprising: atemperature monitoring circuit for measuring a plurality of temperaturesof said electrochemical cell; a voltage monitoring circuit for measuringa plurality of open circuit voltages of said electrochemical cellcorresponding to said plurality of temperatures, said plurality of opencircuit voltages generated upon charging or discharging saidelectrochemical cell or stopping charging or discharging saidelectrochemical cell; a thermodynamic measurement circuit fordetermining thermodynamic parameters of said electrochemical cell,wherein said thermodynamic parameters are change in enthalpy (ΔH) ofsaid electrochemical cell, a change in entropy (ΔS) of saidelectrochemical cell and/or a change in free energy of saidelectrochemical cell (ΔG); wherein said thermodynamic measurementcircuit is positioned in electrical or data communication with saidvoltage monitoring circuit to receive said open circuit voltagemeasurements and positioned in electrical or data communication withsaid temperature monitoring circuit to receive said temperatures; and astate of charge calculating circuit for determining the state of chargeof said electrochemical cell positioned in electrical or datacommunication with said thermodynamic circuit to receive saidthermodynamic parameters; wherein said state of charge calculatingcircuit determines a state of charge of said electrochemical cell usingsaid thermodynamic parameters and a multidimensional state of chargeprofile for said electrochemical cell. 61-62. (canceled)
 63. The deviceof claim 60, wherein said device further comprises a current monitoringcircuit for measuring a charging current of said electrochemical cell ora discharging circuit current of said electrochemical cell, wherein saidcurrent monitoring circuit is positioned in electronic or datacommunication with said thermodynamic circuit and said state of chargegenerating circuit.
 64. The device of claim 60, wherein saidthermodynamic measurement circuit determines a change in enthalpy (ΔH)and a change in entropy (ΔS) for said electrochemical cell, wherein saidstate of charge calculating circuit compares said change in enthalpy(ΔH) and said change in entropy (ΔS) determined for said electrochemicalcell to said multidimensional state of charge profile. 65-69. (canceled)